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**

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**