Question

Jessica deposits $40,000 into an account that pays 4% interest per year, compounded annually. Tom deposits $40,000 into an account that also pays 4% per year. But it is simple interest. Find the interest Jessica and Tom earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits.

Answer 1

Given the principal as $40,000 and rate as 4% we can find the interest below.

Explanation

For Jessica who uses compound interest, we will have

$\begin{gathered} C.I=P(1+\frac{r}{n})^{nt}-p \\ \end{gathered}$

Therefore;

$\begin{gathered} For\text{ }the\text{ }first\text{ }year,we\text{ }will\text{ }have \\ 40000\left(1+\frac{0.04}{1}\right)^{1\cdot\:1}-40000 \\ =40000\cdot\:1.04-40000 \\ =41600-4000=1600 \\ For\text{ t}he\text{ second y}ear,we\text{ w}\imaginaryI ll\text{ h}ave \\ 40000\left(1+\frac{4\%\:}{1}\right)^{1\cdot\:2}-40000 \\ =43264-40000=3264 \\ For\text{ t}he\text{ third y}ear,we\text{ w}\imaginaryI ll\text{ h}ave \\ 40000\left(1+\frac{4\%\:}{1}\right)^{1\cdot\:3}-40000 \\ =44994.56-40000=4994.56 \end{gathered}$

For Tom who uses simple interest

$\begin{gathered} S.I=\frac{PRT}{100} \\ \end{gathered}$$\begin{gathered} For\text{ first year,} \\ S.I=\frac{40000\times4\times1}{100}=1600 \\ Since\text{ it is simple interest the interest would remain the same across the three years} \\ For\text{ second year=1600} \\ For\text{ third year =1600} \end{gathered}$