Question

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.

Answer 1

Answer:

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%