Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The principal amount that was invested is $5576.65.
What is compound interest?
Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount
P is the principal amount
r is the rate of interest
n is the number of times interest is charged in a year
t is the number of years
Given the compound interest is $2,500, while the interest rate is 5% compounded semi-annually for 7.5 years, therefore, the principal amount is,
[tex]A = P(1+\dfrac{r}{n})^{(n \times t)} - P\\\\2500 = P[(1+\dfrac{0.05}{2})^{(2 \times 15)} -1]\\\\P = 5576.65[/tex]
Hence, the principal amount that was invested is $5576.65.
Learn more about Compound Interest:
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