Question

Miranda is renovating her home and needs a $32,000 loan to pay for the renovations. The bank offers her a 4.8% annual compound interest rate if she pays it off in 3 to 5 years. How much more would Miranda pay for the 5 year loan than the 3 year loan?

Answer 1

In 3 years Miranda would pay $36,832.72.

In 5 years Miranda would pay $40,453.53.

Answer 2

$3072

Explanation:

The compound interest formula for the amount paid on the loan P = P₀(1 + rt/100) where P₀ = loan amount = $32,000, r = rate = 4.8 % per annum and t = time

For the 3 year loan, t = 3, So,

P = P₀(1 + rt/100)

P = $32,000(1 + 4.8 × 3/100)

P = $32,000(1 + 14.4/100)

P = $32,000(1 + 0.144)

P = $32,000(1.144)

P = $36608

For the 5 year loan, t = 5, So,

P' = P₀(1 + rt/100)

P' = $32,000(1 + 4.8 × 5/100)

P' = $32,000(1 + 24/100)

P' = $32,000(1 + 0.24)

P' = $32,000(1.24)

P' = $39680

So, the amount more Miranda pay for the 5 year loan than the 3 year loan is P' - P = $39680 - $36608 = $3072