Question

Cindy inherited some money from her grandfather and it put it in a bank account that's earns 7% interest compounded quarterly after 8 years Cindy had $10,000.00 in the bank account. how much interest did she earn

Answer 1

How much interest Cindy earn?

We know that the we can calculate the amount of the total amount of money in the bank, A, is given by the formula

$A=P(1+\frac{r}{n})^{nt}$

where

P = Principal investment amount

r = the annual interest rate

n = the number of times that interest is compounded per year

t = the time the money is invested or borrowed for

We know that

A = $10,000

P = ?

r = 7/100 = 0.07

n = 4

t = 8 years

We replace those values in the equation

$\begin{gathered} 10,000=P(1+\frac{0.07}{4})^{4\cdot8} \\ 10,000=P(\frac{4.07}{4})^{32} \\ 10,000=(1.0175)^{32}P \\ 10,000=1.7422135P \\ 5,739.82=P \end{gathered}$

Since the Principal investment amount is $5,739.82 is the money she put in the bank, then she earn $10,000 - $5,739.82 = $4,260.18

Answer: She earned $4,260.18