Chapter 5.7, Problem 11AYU

$\$1200$ Invested at $5\%$ compounded daily after a period of $3$ years.

To determine

To calculate: The amount that results from investment if $\$1200$ invested at $5\%$ compound daily after a period of $3$ years.

Answer to Problem 11AYU

Solution:

The amount results from investment is $\$1394.19$

Explanation of Solution

Given information:

Principal amount $P=1200$

Compounded interest rate per annum $r=0.05$

Number of times the interest compounded per annum $n=365$

Amount compounded for number of years $t=3$

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

Calculation:

Use the compound interest formula with $P=1200$, $r=0.05$, $n=365$ and $t=3$ to find A.

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

$A=1200{\left(1+\frac{0.05}{365}\right)}^{(365\cdot 3)}$

$A=1200\cdot {(1+0.00013699)}^{1095}$

$A=1394.19$

Hence, the amount results from investment of $\$600$ at $5\%$ interest rate, compounding quarterly after a period of $3$ years is $\$1394.19$