maya invested $110 in an account paying an interest rate of 5% compounded daily. assuming no deposits or…

maya invested $110 in an account paying an interest rate of 5% compounded daily. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 15 years?

maya invested $110 in an account paying an interest rate of 5% compounded daily. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 15 years?

Answer

Explanation:

Step1: Recall compound interest formula

The formula for compound interest is: $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ Where:

  • $A$ = final amount
  • $P$ = principal amount ($$110$)
  • $r$ = annual interest rate (5% = $0.05$)
  • $n$ = number of times interest is compounded per year (365, for daily compounding)
  • $t$ = time in years (15)

Step2: Plug in the values

Substitute the known values into the formula: $$A = 110\left(1 + \frac{0.05}{365}\right)^{365 \times 15}$$

Step3: Calculate intermediate values

First compute $\frac{0.05}{365} \approx 0.000136986$, then $1 + 0.000136986 \approx 1.000136986$. Next calculate the exponent: $365 \times 15 = 5475$.

Step4: Compute the final amount

Calculate $(1.000136986)^{5475} \approx 2.11700$, then multiply by 110: $$A \approx 110 \times 2.11700 = 232.87$$

Answer:

$$232.87$