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# 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 