Question

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.

Answer 1

Oliver withdraws an amount of $285.10 from his saving account

Oliver's savings account accrues an annual interest rate of 1.8%. Calculating the monthly interest involves dividing this by 12, resulting in 0.018 or 3/2000.

After five months, the total amount in the account is found using the formula

A = P(1 + r/n)ⁿ,

where A is the final amount,

P is the principal,

r is the monthly interest rate, and

n is the number of months.

For Oliver's account with a principal of $285.10, the final amount after five months is $311.70.

The interest earned is determined by subtracting the initial principal from the final amount, yielding $26.60.

Therefore, Oliver could have earned $26.60 in interest over the five-month period.

Answer 2

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