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.
275
likes1375 views
Answer to a math 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.
Jett
4.792 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.
Frequently asked questions (FAQs)
Math Question: What is the value of x in the equation log(x) + log(x + 5) = 3?
+
Q: What is the period of the cosine function f(x) = cos x?
+
What is the smallest value of n that satisfies Fermat's theorem equation: a^n + b^n = c^n for integers a, b, and c, where n > 2?
+
New questions in Mathematics