Question

What is the time period and rate if $12000 is borrowed for 2 years at 4% p.a. compounded quarterly?

Answer 1

Answer: t = 2, r = 4%, A = $12,994.28

Explanation:

The formula for compound interest is:
`A=P_o\bigg(1+(r)/(n)\bigg)^(nt)` where

• A is the accrued amount
• P₀ is the principal (initial amount invested)
• r is the rate (convert percent into a decimal)
• n is the number of times per year the interest is compounded
• t is the number of years the principal is invested

The information provided in the given problem is:

• P₀ = 12,000
• r = 4% ⇒ 0.04
• n = quarterly ⇒ 4
• t = 2

`A = 12,000\bigg(1+(0.04)/(4)\bigg)^(4\cdot 2)\\\\.\quad =12,000(1+0.01)^(8)\\\\.\quad =12,000(1.01)^(8)\\\\.\quad =12,994.28`