Mrs. Williams finds that she has two options for investing $32000.02 for fifteen

Question

Mrs. Williams finds that she has two options for investing $32000.02 for fifteen years. The first option is to deposit it into a fund earning a nominal rate of discount d(4) payable quarterly. The second option is to purchase an annuity-immediate with 15 level annual payments, the annuity payments computed using an effective annual interest rate of 7%, and then when she gets the annuity payment,, to immiedetly invest it into a fund earning an annual effective rate of 5%. She calculates that the second option produces and accumulated value that is $1,500 more than the accumulated value yielded by the first option. Calculate d(4).


- The answer is 5.57790%, just need to show the work!

Thanks in advance

Explanation / Answer

2nd option:
Use 32,000.02 to buy annuity
Let A = Annuity she will received each year
32,000.02 = (A/0.07)(1-1/1.0715)

A = 3513.43

Reinvest this amount at interest rate of 5%

FInal value = 3513.43{(1.0514)+(1.0513)+...+1.05+1) = 75,814.77

Value of the first option = 75,814.77 - 1,500 = 74,314.77

74,314.77 = 32000.02(1+d^4/4)15*4

d^4 = 0.05656    ( rounding error)

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