Question

A business pays $5,250 in interest for a loan over 5 years. If the interest rate is 7.5% compounded annually, what was the original amount of the loan that the business borrowed?

Answer 1

Case: Compound Interest

Method:

Compound Interest,

C.I= $5,250

t= 5 years

r= 7.5%

n= 1 (annually)

`\begin{gathered} Amount, \\ A=P(1+(r)/(n))^(nt) \\ P+C.I=P(1+(r)/(n))^(nt) \\ P+5250=P(1+(0.075)/(1))^(1(5)) \\ P+5250=P(1+0.075)^5 \\ P+5250=P(1.075)^5 \\ P+5250=1.436P \\ 1.436P-P=5250 \\ 0.436P=5250 \\ P=(5250)/(0.436) \\ P=12051.53 \end{gathered}`

Final answer:

P= $12051.53

the original amount of the loan that the business borrowed was $12051.53