bob and barbara are friends. bob takes out a $10000 loan and agrees to repay it over 12 years making annual level payments at an effective rate of 5.62499%. at the same time barbara takes out a $10000 loan and agrees to repay it by making annual interest payments at an annual effective interest rate of i. she also agrees to make annual level deposits into a sinking fund that earns 4% annual effective interest so as to accumulate $10,000 at the end of the 12 years. bob and barbara discover they have the same total annual expenditures resulting from their loans. find the rate i.

Question

Amir Lowe

Business

13 March, 13:19

bob and barbara are friends. bob takes out a $10000 loan and agrees to repay it over 12 years making annual level payments at an effective rate of 5.62499%. at the same time barbara takes out a $10000 loan and agrees to repay it by making annual interest payments at an annual effective interest rate of i. she also agrees to make annual level deposits into a sinking fund that earns 4% annual effective interest so as to accumulate $10,000 at the end of the 12 years. bob and barbara discover they have the same total annual expenditures resulting from their loans. find the rate i.

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Lilah Cowan · Answer 1

5.0285%

Explanation:

Bob's annual payment is $1,168.37 (using a financial calculator)

Barbara's annual interest payment = $1,168.37 - annuity that will have a future value of $10,000 in 12 years

future value of annuity = payment x [ (1 + r) ⁿ - 1] / r

r = 4% future value = $10,000 n = 12

$10,000 = payment x [ (1 + 0.04) ¹² - 1] / 0.04

$10,000 = payment x 15.0258

payment = $10,000 / 15.0258

payment = $665.52

Barbara's annual interest payment = $1,168.37 - $665.52 = $502.85

Barbara's effective interest rate i = $502.85 / $10,000 = 5.0285%