Question

A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.

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Jett

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41 Answers

Given:
Total amount=A=1900.
Principal amount=P=1000.
annual interest rate=r=0.1%.
Compound interest:
A=P\left(1+\frac{r}{100}\right)^n
Substitute the given values in above formula, we get
1900=1000\left(1+0.1\right)^n
1.1^n=\frac{1900}{1000}
1.1^n=1.9
apply natural logarithm on both sides, we get
\ln\left(1.1^n\right)=\ln\left(1.9\right)
n\cdot\ln\left(1.1\right)=\ln\left(1.9\right)
n=\frac{\ln\left(1.9\right)}{\ln\left(1.1\right)}
n=6.734.
Therefore, The duration of the loan in compounding period is 6.734.

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