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%

Answer 2

Based on the information given, the effective interest rate will be 5.0285%.

From the information given, by using a financial calculator, Bob's annual payment will be $1,168.37.

Also, the future value of annuity will be calculated thus:

= payment x [(1 + r)ⁿ - 1] / r

where,

r = 4%

future value = $10,000

n = 12

Therefore, this will be

$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

Therefore, Barbara's annual interest payment will be calculated thus:

= $1,168.37 - $665.52

= $502.85

Therefore, her effective interest rate will be:

= $502.85 / $10,000

= 5.0285%

In conclusion, the correct option is 5.0285%.

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