Answered

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 :

SOLUTION:

Case: Compound Interest

Method:

Compound Interest,

C.I= $5,250

t= 5 years

r= 7.5%

n= 1 (annually)

[tex]\begin{gathered} Amount, \\ A=P(1+\frac{r}{n})^{nt} \\ P+C.I=P(1+\frac{r}{n})^{nt} \\ P+5250=P(1+\frac{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=\frac{5250}{0.436} \\ P=12051.53 \end{gathered}[/tex]

Final answer:

P= $12051.53

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

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