Question

Please answer the ??? on questions A, B, and C

A. Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time.

$678 per month invested at 6%, compounded monthly, for 3 years; then $784 per month invested at 7%. compounded monthly for 3 years.

What is the amount in the account after 6 years ??? ​(Round to the nearest dollar as​ needed.)

B. Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time.

$1300 per quarter invested at 4.2%, compounded quarterly for 10 years; then $1900 per quarter invested at 4.4% compounded for 16 years.

Find the final amount in the account.??? (Round to the nearest dollar as​ needed.)

C. Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period.

$60,000 to be accumulated in 9 years; annual payments of $5047.

The interest rate needed is approximately ??? % ​(Round to two decimal places as​ needed.)

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Answer 1

The answer has been presented in the supporting sheet. For detailed answer refer to the supporting sheet.

A B C D E G H Answer Part A) The amount in account after 6 Years = ((678* Future value annuity (36,(6%/12))*(1+(7%/12))^36)+(784*Future value annuity(36, (7%/12))) = ((678*(((1.005)^36-1)/.005)) *1.232926)+(784*(((1.005833)^36-1)/.005833)) = 32882+31305.2 = $ 64187 (rounded off to 0 decimal places) Thus the correct answer amount in retirement account $64187 Part b) The amount in account after 26 Years = ((1300* Future value annuity (40,(4.2%/4))*(1+(4.4%/4))^64)+(1900*Future value annuity(64 (4.4%/4))) = ((1300*(((1.0105)-40-1)/.0105))*2.014067)+(1900*(((1.011) "64-1)/.011)) = 129326.6 +175157.1 = $ 304484 Thus the correct answer amount in retirement account $ 304484 Partc) Future value annuity fatcor (i%,9) = amount to be accumulated / annual payment = 60000/5047 = 11.88825 = From factor table it can be concluded that this annuity is for 6.82% - Thus the correct answer is 6.82% Sheet1