Question

Aubrey took out a loan from a bank at 3% interest compounded quarterly after 2 years the balance on the loan was $8,000.00. How much interest had accumulated on the loan?

Answer 1

For this kind of scenario, let's apply the Quarterly Compounding Formula:

$A\text{ = }P\lbrack(1+r)^{4n}\rbrack$

Where,

A = The total balance of the loan including the interest = $8,000.00

P = Principal Amount (Loan amount)

r = Rate of interest = 3%

n = No. of periods = 2 years

Let's plug in the values to the formula. we get,

$\text{ A = }P\lbrack(1+r)^{4n}\rbrack\text{ }\rightarrow\text{ 8,000 = }P\lbrack(1+\frac{3}{100})^{4(2)}\rbrack$$\text{8,000 = }P\lbrack(1+0.03)^{8)}\rbrack\text{ }\rightarrow\text{ 8,000 = }P\lbrack(1.03)^8\rbrack$$\text{8,000 = }P\lbrack(1.03)^8\rbrack\text{ }\rightarrow\text{ 8,000 = P(1.26677008139)}$$\text{P = }\frac{8,000}{\text{1.26677008139}}\text{ = \ 6,315.27}$

We now get the accumulated interest:

$\text{ Accumulated Interest = A - P = \ 8,000 - \ 6,315.27}$$\text{ Accumulated Interest = \ 1,684.73}$

Therefore, Aubrey accumulated a total of $1,684.73 interest.