Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The account balance after a period of 5 years will be $1.63634×10²⁰.
<h3>What is compound interest?</h3>
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.
![A = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Given the principal amount is $12,385, the rate of interest is 7.5%, and the time period is daily. Therefore, the amount can be written as,
![A = P(1 + \frac{r}{n})^{nt}\\\\A = \$12,385(1 + \frac{7.5}{365})^{(365 \times 5)}\\\\A = \$1.63634 \times 10^{20}](https://tex.z-dn.net/?f=A%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%5C%5C%5C%5CA%20%3D%20%5C%2412%2C385%281%20%2B%20%5Cfrac%7B7.5%7D%7B365%7D%29%5E%7B%28365%20%5Ctimes%205%29%7D%5C%5C%5C%5CA%20%3D%20%5C%241.63634%20%5Ctimes%2010%5E%7B20%7D)
Hence, the account balance after a period of 5 years will be $1.63634×10²⁰.
Learn more about Compound Interest:
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