Question

If $163,300 is invested in an account earning 3.75% annual interest compounded semi-annually, how much interest is accrued in the first 4 years? Round to the nearest cent?

Answer 1

An amount compounded is given as;

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \text{Where;} \\ P=\text{ amount invested;} \\ r=\text{ interest rate;} \\ n=\text{ number of times interest applied per time period;} \\ t=\text{ number of time period elapsed.} \end{gathered}`

Given that;

`\begin{gathered} P=163,300 \\ r=0.0375 \\ n=2 \\ t=4 \end{gathered}`

Thus, we have;

`\begin{gathered} A=163300(1+(0.0375)/(2))^(2*4) \\ A=163300(1.01875)^8 \\ A=189464.20 \end{gathered}`

Thus, the interest accrued in the first 4 years is;

`\begin{gathered} I=A-P \\ I=189464.20-163300 \\ I=26164.20 \end{gathered}`

FINAL ANSWER: $26,164.20