AFF 210 Lecture Notes - Lecture 4: Interest, Savings Account

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rubyrat622

28 Mar 2016

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Simple interest: fv = pv + pv(i)(n) same amount of interest each year. Compound interest: interest earned on top of interest; always earn more/lose more money in interest. Annuities equal payments made at fixed intervals for finite number of periods. Ordinary annuity: payments made at the end of each period. Annuity due: payments at beginning of each period the pv of each payment would be larger since each payment would be discounted 1 year less making the pv of annuity also larger. Also the fv of annuity due would be larger; each payment would be compounded for an extra year. Fv of annuity due = fva ordinary x (1+i) Pv of annuity due = pva ordinary x (1+i) Perpetuities annuity whose payments are extended out forever. Interest rates can be found if the cash flows & the pv or fv of the cash flows is known.

Related Questions

CAN SOMEONE LET ME KNOW IF I DID THESE RIGHT?? PLEASE

1. What is the effective rate of interest for an investment paying 18% compounded monthly?

Effective rate of interest= (1+r)^n-1

r= 18% or .18; compounded monthly= 0.18/12

N= no of period ie 12

Effective rate r= (1+.18/12)^12-1

= 0.1956 ie 19.56%

2. If you want to buy a $25,000 car in 5 years, what single amount must you invest now at 10% compounded quarterly to have the money to pay cash?

Fv= PV(1+i)^n

Fv= 25,000 n=5 years so 5*4= 20 periods; r = 10% compounded quarterly ie .10/4

25,000=PV(1+.10/4)^20

25,000= PV (4.10/4)^20

PV= (25,000/1.025)^20

PV=$15,256.77

3. What is the present value of $50,000, 4 years from now at 12% interest compounded monthly?

Fv= Pv (1+r)^n

Fv=50,000; Pv?; n= 4 years compounded monthly ie 48; R= 12% compounded monthly ie .12/12

50,000= PV (1+.12/12)^48

PV=50,000/(1.01)^48

PV=$31,013.02

4. What is the future value of $5,000 in 15 years if you can earn 12% interest compounded semi-annually?

Fv=PV(1+i)^n

Fv=5,000; n=15 years semi annually= 30 periods; I=12% compounded semi annually=.12/2

5,000= PV (1+.12/2)^30

PV=5,000(1.06)^30

PV=$28,717.46

5. What is the future value of $800 deposited annually at 9% interest for 25 years if the deposits are made at the end of the period? And, if the deposits are made at the beginning of the period?

FV(end)= PMT[(1+i)^n-1)/i] (Ordinary annuity)

FV= $800; i=9% or .09; n=25 years

Fv+800[(1+0.09)^25-1)/0.09

FV=$67,760.72

FV=(beginning)= PMT[((1+i)^n-1)/i](1+r)

FV=$800; I=9% or 0.09; n=25 years

FV=800[(1+0.09)^25-1)/0.09)(1+0.09)

FV=$73,859.18

6. Using the information from the previous problem, how much more interest is earned from the annuity due than from the ordinary annuity?

Annuity due= annuity (beginning) - ordinary annuity

=$73,859.18-$67,760.72= $6,098.46

7. How much must be deposited now in order to withdraw $15,000 at the end of each year for 30 years, if interest is 11% compounded annually?

Annuity the end of each year= 15,000

N=30 years; r= 11% compounded annually

To find PV of an annuity of $15,000 @ the end of each of the year

PV= PMT [1-(I+i)^-n/i

PV=15,000[1-(I+0.11)^-30/0.11]

PV= PMT[1-(I+i)^-n/i

=$130,406.89

8. If you want $2,000,000 in your retirement fund in 45 years, and you can earn 14% compounded annually, what will be your annual contribution? How much interest will you earn?

FV= 2,000,000; N= 45 years; i= 14% compounded annually

We have the FV of an annuity â to find the annuity

FV= PMT [(I+i)^n-1)/i]

2,000,000=PMT [((1+0.14)^45-1)/(0.14]

2,000,000= PMT [2590.5648]

PMT=$772.03

9. If you retire with $1,375,000 in your retirement fund and plan to live for 20 years, how much can you withdraw every year if your investment earns 10%?

PV= 1,375,000 n=20 years i=10%

To find annuity given the PV

PV=PMT [1-(1+i)^-n/I]

1,375,000= PMT [1-(1+0.10)^-20/0.10)

PMT(yearly withdrawl) =$161,506.98

10. How much more interest is earned from ordinary annuity payments of $6,000 per year for 25 years if you can increase your rate of interest from 6% to 9%?

PMT=$6,000 per year; n=25 years; i=6% to 9%

Interest at 6%

FV= PMT [((1+r)^25-1)/0.06]

FV= 6,000[((1+0.06)^25-1)/0.06]

=$329,187.07

Interest at 9%

FV=6,000[(91+0.09)25-1)/0.09]

= $508,205.38

More earned interest 9%- 6% = $508,209.38 - $329,187.07 = $179,018.31

sapphiresnake702

4.3	Need help with 4.4 a and b at bottom. 4.3 is required to answerthis. Calculate the following values, assuming a discount rate of8%:
	a.	present value of a perpetuity (also called a perpetual annuity)of $50 received each year at the end of each year
	b.	present value of an annuity of $50 received at the end of eachyear for 5 years
	c.	present value of an annuity of $50 received at the end of eachyear for 10 years, with the first payment to be received at the endof the 6^th year
	d.	present value of a perpetuity of $50, with the first paymentreceived at the end of the 16^th year. *ANSWER:* a. PV of perpetuity = A/i where A is annual payment &i is disc rate SO PV of Perpetuity = 50/8% = $625.00 b. Here it is PV of annuity for n=5 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,5). From PV of annuity Table, we get (PVIFA8%,5) = 4.3295 So PVA = 504.3295 = $216.48 c. This has 2 parts. First Find the PV of Annuity at 6 yrs &then find the PV of that amount at T0. Here it is PV of annuity for n=10 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,10). From PV of annuity Table, we get (PVIFA8%,5) = 6.7101 So PVA = 506.7101 = $335.51 Now PV = FV/(1+i)^n = $335.51/(1+8%)^6 = $211.43 d. This has 2 parts. First Find the PV of Perpetuity at 16 yrs& then find the PV of that amount at T0. PV of Perpetuity = A/i = 50/8% = $625 Now PV of this amount PV = 625/(1+8%)^16 = $182.43
4.4	a.	Show (with a time line, for example) that the perpetuity in4.3a. is exactly the same as the sum of the annuities andperpetuities in 4.3b. to 4.3d.
	b.	Show that their present values add up to the same amount.

violetpig294

Assume that you have $1,000 to invest, so insert 1000 as your Present Value in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $1.159, which is what your investment will be worth in 5 years. Now revise the input to reflect your actual savings and the prevailing interest rate so that you can see how your savings will grow in 5 years. Even if you have no savings now, you can at least see how the interest rate affects the future value of savings by revising your input in the Interest Rate per Period and then observing the change in the Future Value. Future Value of a Present Amount Present Value $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = PV*(1+R)^N Future Value $1,739 2. Assume that you have $1,000 to invest at the end of each of the next 5 years, so insert 1000 as your Payment per Period in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $5,309, which is what your investments will be worth in 5 years. Now revise the input to reflect your actual expected savings per year over the next 5 years, and existing interest rate quotations so that you can estimate how your savings will grow in 5 years. You can now revise the table to fit your own desired level of saving. Future Value of an Annuity Payment per Period $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = FV(R, N, PMT, (PV), beginning=1, end=0) Future Value $7,964 3. Assume that you want to deposit savings that will be worth $10,000 in 5 years, so insert 10000 as the Future Amount and 5 as the Number of Periods in the following table. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Present Value, which represents the amount of savings you need today that would accumulate to be worth $10,000 in 5 years. If you input the numbers correctly, the Present Value is estimated in the table to be $8,606. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need now to achieve your savings goal in 5 years. Present Value of a Future Amount Future Amount $20,000 Number of Periods 5 Interest Rate per Period 3.0% PV = FV / (1+R)^N Present Value $17,252 4. Assume that you want to deposit savings at the end of each of the next 5 years so that you will have $10,000 in 5 years. So insert 10000 as the Future Amount and 5 for Number of Periods. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Annual Payment, which represents the annual payments that will accumulate to your future desired investment. If you input the numbers correctly, your Annual Payment is computed to be $1,884. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need to save per year to achieve your savings goal in 5 years. Compute Payment Needed to Achieve Future Amount Future Amount $20,000.00 Number of Periods 5.00 Interest Rate per Period 3.00% PMT = FV / [FV(R, N, -1)] Annual Payment $3,767

Decisions 1. Using the above formulas and understanding of the impact of interest rates and time on your savings, report on how much you must save per year and the return you must earn to meet your savings goal for graduation, and your savings goal in your first three years of post-graduation life.

I need a report on how much to save per year and the return to earn to meet savings goal for graduation, and savings goal in the first three years of post graduation. Can you please use the numbers above that are already calculated in the formula. I have had an answer on this below. I don't understand why the periods don't stay the same for 5 years. The annuity is 7964 I took that divided b y 60 = 132.7 per month and multiplied it by 12 for a year and got 1592.4. Is that the savings for the answer to saving for a year. IF not I need help figuring out the calculation for the return to meet after gradutaion and the next three years post graduation.

Goal 1	Savings Goal for graduation, FV	$ 20,000

	Time till graduation (Number of periods)	5

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$3,767.09	=PMT(3%,5,0,20000,)

Goal 2	Savings Goal for 1st year of post graduation, FV	$ 15,000

	Time till post graduation year 1 (Number of periods)	6

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$2,318.96	=PMT(3%,6,0,15000,)

Goal 3	Savings Goal for 2nd year of post graduation, FV	$ 15,300

	Time till post graduation year 1 (Number of periods)	7

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$1,996.75	=PMT(3%,7,0,15300,)

Goal 4	Savings Goal for 3rd year of post graduation, FV	$ 15,606

	Time till post graduation year 1 (Number of periods)	8

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$1,754.99	=PMT(3%,8,0,15606,)

AFF 210 Lecture Notes - Lecture 4: Interest, Savings Account

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