Question

Brian deposited $7,330 into a savings account for which interest is compoundeddaily at a rate of 3.43%. How much interest will he earn after 5 years? Roundanswer to the hundredths place.

Answer 1

SOLUTION

To solve this, we use the compound interest formula

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Where\text{ A = amount after 5 years = ?} \\ P=principal\text{ or money deposited = \ 7,330} \\ r=interest\text{ rate = 3.43\%} \\ n=number\text{ of times compounded = 365, that is daily for a year} \\ t=\text{ time in years = 5} \end{gathered}$

Plugging in the values into the formula, we have

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=7,330(1+\frac{\frac{3.43}{100}}{365})^{365\times5} \\ A=7,330(1+\frac{0.0343}{365})^{1,825} \\ A=7,330(1.00009397)^{1,825} \end{gathered}$

Continuing we have

$\begin{gathered} A=7,330(1.000,093,97)^{1,825} \\ A=7,330\times1.1870745776 \\ A=8,701.256654 \\ A=8,701.26 \end{gathered}$

Hence the answer is $8,701.26 to the nearest hundredths