annabelle invested $87,000 in an account paying an interest rate of 1.6% compounded daily. assuming no…

annabelle invested $87,000 in an account paying an interest rate of 1.6% compounded daily. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 16 years?

annabelle invested $87,000 in an account paying an interest rate of 1.6% compounded daily. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 16 years?

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula when compounded (n) times a year is (A = P(1+\frac{r}{n})^{nt}), where (P) is the principal amount, (r) is the annual interest rate (in decimal form), (n) is the number of times interest is compounded per year, and (t) is the number of years.

Given (P=$87000), (r = 1.6%=0.016), (n = 365) (compounded daily), and (t = 16) years.

Step2: Substitute the values into the formula

[ \begin{align*} A&=87000\left(1+\frac{0.016}{365}\right)^{365\times16}\ &=87000\left(1 + 0.0000438356\right)^{5840}\ &=87000\times(1.0000438356)^{5840} \end{align*} ]

Step3: Calculate ((1.0000438356)^{5840})

Using a calculator, ((1.0000438356)^{5840}\approx1.2877)

Step4: Calculate (A)

[ A=87000\times1.2877 = 112029.90 ]

Answer:

(112029.90)