Question

 Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of​ research, Jill Moran. Ms.​ Moran, by​ contract, will retire at the end of exactly 12 years. Upon​ retirement, she is entitled to receive an annual​ end-of-year payment of $ 42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12 year "accumulation period," Sunrise wishes to fund the annuity by making​ equal, annual, ​ end-of-year deposits into an account earning 9.0 % interest. Once the 20 year "distribution period"​ begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12.0% per year. At the end of the distribution​ period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13.

To Do

a. Draw a time line depicting all of the cash flows associated with​ Sunrise's view of the retirement annuity.

b. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?

c. How large must​ Sunrise's equal, ​ annual, end-of-year deposits into the account be over the 12​-year accumulation period to fund fully Ms.​ Moran's retirement​ annuity?

d. How much would Sunrise have to deposit annually during the accumulation period if it could earn

10.0 % rather than 9.0 % during the accumulation​ period?

e. How much would Sunrise have to deposit annually during the accumulation period if Ms.​ Moran's retirement annuity were a perpetuity and all other terms were the same as initially​ described?

Answer 1

Answer to question no a

Sunrise will have to pay for first 12 years (accumulation period) then next 20 year fund will be transferred to other interest earning account hence Sunrise will have to pay till 13th years. After accumulation period is over, Ms. Moral will be paid automatically from investment to 12% interest earning fund.

Answer to question no b

In the question, we have few information available as shown below

Annuity Amount = $42000

Total Tenure/period= 20 Years

Interest rate =12% or say 0.12 annual

We need to find out the investment amount and formula is as shown below

Investment Amount = EMI amount/(rate*(1+rate)^(Period)/((1+rate)^Period-1)

= $42000/(0.12*(1+0.12)^20/((1+0.12)^20-1

=$42000/0.12*(1.12)^20/(1.12)^19

=$42000/0.1344y

=$312500

** You can take help of calculator or use excel to compute the above calculation.

Answer is that Sunrise have to accumulate a sum equal to $312500 by end of year 12 to provide the 20 year, $42000 annuity

Answer to question no c

In the question, we have following information

Period = 12 years

Interest rate = 9%

Principal + Interest= 312500

Here, we need to find out the principal amount every year to get the sum of $312500 or say present value of $312500

The applicable formula to get the present value loan is as shown below

Present Value = Maturity Amount*((1/)(1+Rate)^Period)

= $312500*(1/(1+.09)^9)

= $143883.68 ( rounded off)

Kindly check the calculation with help of calculator

Answer is that Sunrise need to a total sum of $143883.68 and annual amount is $143883.68 /12= $11990 every year

Answer to question no d

If interest rate is as more as 10% instead of 9%, then less amount to be invested by Sunrise and in the same formula, we need to replace the rate as 0.10 against 0.09 and we will get the amount as $99572.

Answer is $99572

Answer to question no e

Have already mentioned the annual investment in answer to question no c and that is $11990.