Oliver is buying a new dishwasher. The dishwasher’s price is $285.10 after tax. He has a few payment options. He can put it on his debit card, which would take the money from his savings account. His savings account earns interest at a rate of 1.8% annually. He could also put it on one of two different credit cards. Card A has an annual interest rate of 9%, charged monthly, and charges a flat 1.2% fee on the initial value of the purchase (note: the fee accrues interest too). Card B has an annual interest rate of 12%, charged monthly, but no fee for purchases. Oliver thinks it will take five months for him to earn the additional money to offset the purchase. In all cases, the interest accrues according to this equation: A = P(1 + r)n, where A is the final dollar amount, P is principle (initial amount borrowed), r is the interest rate for each interest period, and n is the number of interest periods. If Oliver withdraws $285.10 from his savings account to make the purchase, how much would he have earned in interest on that amount over five months? Round your answer to the nearest cent.

Respuesta :

Oliver withdraws an amount of $285.10 from his saving account

His saving account earns 1.8% annually

The interest Oliver could have earned in five months:

Monthly interest = Annual interest ÷ 12
Monthly interest = 1.8% ÷ 12
Monthly interest = 0.018 ÷ 12 = 3/2000

After five months = Principle × (1 + interest)ⁿ
After five months = 285.10 × (1 + 0.018)⁵
After five months = 311.70

Interest earned = 311.70 - 285.10 = $26.60