1. What is the effective rate of interest for an investment paying 18% compounde

Question

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

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?

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

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

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?

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

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?

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?

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%?

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%?

Explanation / Answer

effective rate of interest = (1 + r) ^n -1 Where r - rate of interest; here r = 18% - 0.18; compounded monthly= 0.18/12; N = no of period ie 12 Effective rate r = (1+0.18/12)^12 - 1 = 0.1956 ie 19.56% 2.Fv = PV (1 + i)^n Fv = 25000' n = 5 years so 5 * 4 = 20 periods; r = 10% p.a. comp. quarterly ie 0.10 /4 25000 = PV ( 1 + 0.10/4)^20 25000 = PV (4.10/4)^20 PV =( 25000 / 1.025 )^20 PV = $ 15256.77 3. FV = PV (1 + r)^n FV = 50000; PV ?; n 4 years comp month ie 48; R = 12% comp monthly ie 0.12/12 50000 = PV (1 + 0.12/12)^ 48 PV = 50000 / (1.01)^48 = $ 31013.02 4.Fv = PV (1 + i)^n Fv = 5000; n = 15 years semi annually = 30 periods; I = 12% comp semi annually = 0.12/2 5000 = PV (1 +0.12/2)^30 PV = 5000 (1.06)^30 PV = 5000 (1.12)^30 PV = $ 28717.46 5. FV (end) = PMT [ ( (1+i)^n - 1 ) / i ]                             (ordinary annuity) FV = $ 800; I = 9% interest = 0.09; n = 25 years Fv = 800 [( 1 + 0.09)^ 25 - 1) / 0.09) FV = $ 67760.72 FV (beginning ) = PMT [ ( (1+i)^n - 1 ) / i ] (1 + r)                            ( annuity at the end) FV = $ 800; I = 9% interest = 0.09; n = 25 years Fv = 800 [( 1 + 0.09)^ 25 - 1) / 0.09) (1 +0.09) FV = $ 73859.18 6. Annunity due = Annunity (beginning) - Oridinary annuity      = $ 73859.18 - $ 67760.72 = $ 6098.46 7 7. Annuity the end of the each year = 15000 n = 30 years;r = 11% comp annually To find PV of an annuity of $ 15000 @ the end of each of the year PV = PMT [ 1 - (I + i ) ^-n / i ] PV = 15000 [ 1 - (I + 0.11 ) ^-30 / 0.11 ] PV = PMT [ 1 - (I + i ) ^-n / i ] = $ 130406.89 8. FV = 2000000 ; n = 45 yeears ; I = 14% comp annually We have the FV of an annuity - to find the annuity FV = PMT [ (I + i ) ^n-1) / i] 2000000 = PMT [ (( 1 +0.14)^45 - 1) /(0.14] 2000000 = PMT [ 2590.5648 ] - PMT = $ 772.03 9. PV = 1375000 n 20 yeARS . 10% P A TO FIND ANNUITY GIVEN THE PV PV = PMT [ 1 - (1 + i)^-n / I ] 1375000 = PMT [ 1 - (1 +0.10)^-20 /0.10) PMT (yearly withdrawal)= $ 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 = $ 6000 per year ; n 25 years ; I = 6% to 9% Interest at 6% FV = PMT [ ((1+r)^25 - 1) /0.06 FV = 6000 [ ((1 + 0.06)^25 - 1)/0.06] = $ 329,187.07 FV = 6000 [ (91 + 0.09) 25 -1) /0.09 = 508,205.38 More earned interest 9% - 6% = $ 508209.38 - $329187.07 = $ 179,018.31

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.