4. (a) If you will be making equal deposits into a retirement account for 10 yea

Question

4. (a) If you will be making equal deposits into a retirement account for 10 years (with each payment at the end of the year), how much must you deposit each year if the account earns 5% compounded annually and you wish the account to grow to $1,000,000 after 30 years (in time 30)? (b) How does your answer to part (a) change if the account pays interest compounded monthly at an annual rate of 5%? Note: use monthly compounding for all calculations. 5. (a) You belong to an unusual pension plan because your retirement payments will continue forever (and will go to your descendants after you die). If you will receive $48,000 per year at the end of each year starting 30 years from now (i.e., the first payment is in time 30), what is the present value of your retirement plan if the discount rate is 5%? (b) How does your answer to part (a) change if you receive $4,000 per month every month forever (in perpetuity) starting 30 years from today (in monthly time period 360) and you compound monthly? 4. (a) If you will be making equal deposits into a retirement account for 10 years (with each payment at the end of the year), how much must you deposit each year if the account earns 5% compounded annually and you wish the account to grow to $1,000,000 after 30 years (in time 30)? (b) How does your answer to part (a) change if the account pays interest compounded monthly at an annual rate of 5%? Note: use monthly compounding for all calculations. 5. (a) You belong to an unusual pension plan because your retirement payments will continue forever (and will go to your descendants after you die). If you will receive $48,000 per year at the end of each year starting 30 years from now (i.e., the first payment is in time 30), what is the present value of your retirement plan if the discount rate is 5%? (b) How does your answer to part (a) change if you receive $4,000 per month every month forever (in perpetuity) starting 30 years from today (in monthly time period 360) and you compound monthly? 4. (a) If you will be making equal deposits into a retirement account for 10 years (with each payment at the end of the year), how much must you deposit each year if the account earns 5% compounded annually and you wish the account to grow to $1,000,000 after 30 years (in time 30)? (b) How does your answer to part (a) change if the account pays interest compounded monthly at an annual rate of 5%? Note: use monthly compounding for all calculations. 5. (a) You belong to an unusual pension plan because your retirement payments will continue forever (and will go to your descendants after you die). If you will receive $48,000 per year at the end of each year starting 30 years from now (i.e., the first payment is in time 30), what is the present value of your retirement plan if the discount rate is 5%? (b) How does your answer to part (a) change if you receive $4,000 per month every month forever (in perpetuity) starting 30 years from today (in monthly time period 360) and you compound monthly?

Explanation / Answer

Ans 4a) After 10 year amount should be in account is given by follwoing formula

1000000 = x* (1+r)^20

where x is the amount after 10 years and

r is interest rate

x = 1000000/(1.05)^20 = $376889.48

x is the future value of the annuity with the help of future vlaue of annuity formula we can find the yearly payment.

FV of annuity = P * ((1+r)^n - 1)/r

376889.48 = P *( (1.05)^10 - 1)/.05

P = $29964.50

Ans b) After 10 year amount should be in account is given by follwoing formula

1000000 = x* (1+r/12)^(20*12)

where x is the amount after 10 years and

r is interest rate

x = 1000000/(1.004167)^240 = $368615.16

x is the future value of the annuity with the help of future vlaue of annuity formula we can find the yearly payment.

FV of annuity = P * ((1+r/12)^(12*n) - 1)/r/12

368615.16 = P * ((1.004167)^120 - 1)/.004167

P = $2369.8

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