Chapter 5.7, Problem 9AYU

$\$900$ Invested at $3\%$ compounded semi-annually after a period of $2\frac{1}{2}$ years.

To determine

To calculate: The amount that results from investment of $\$900$ at $3\%$ interest rate, compounding semiannually after a period of $2\frac{1}{2}$ years.

Answer to Problem 9AYU

Solution:

The amount results from investment of $\$900$ at $3\%$ interest rate compounding semiannually after a period of $2\frac{1}{2}$ years is $\$969.56$.

Explanation of Solution

Given information:

Principal amount $P=900$

Compounded interest rate per annum $r=0.03$

Number of times the interest compounded per annum $n=2$

Amount compounded for number of years $t=2\frac{1}{2}$

Formula used:

The amount A after $t$ years due to a principal $P$ invested at an annual interest rate $r$, compounded $n$ times per year is $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Calculation:

Use the compound interest formula with $P=900$, $r=0.03$, $n=2$ and $t=2\frac{1}{2}=\frac{5}{2}$ to find A.

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

$A=900{\left(1+\frac{0.03}{2}\right)}^{\left(2\cdot \frac{5}{2}\right)}$

$A=900\cdot {(1+0.015)}^5$

$A=969.56$.

Hence, the amount results from investment of $\$900$ at $3\%$ interest rate, compounding semiannually after a period of $2\frac{1}{2}$ years is $\$969.56$