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

To solve this, we use the compound interest formula

`\begin{gathered} A=P(1+(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+(r)/(n))^(nt) \\ A=7,330(1+((3.43)/(100))/(365))^(365*5) \\ A=7,330(1+(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*1.1870745776 \\ A=8,701.256654 \\ A=8,701.26 \end{gathered}`

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