Chapter 7.7, Problem 7P

Find the balance in each account after the giver period.

$500 principal earning 4% compounded quarterly, after 10 yr

To determine

To find the balance of given principal amount after the given period.

Answer to Problem 7P

  $\$\text{744}\text{.43}.$

Explanation of Solution

Given information:

Principal amount (P) = $\$500$ ,

Rate of interest (r) = 4% compounded quarterly.

Time period (t) = 10 years.

Formula Used: Compound interest formula $A=P{\left(1+\frac{r}{n}\right)}^{nt},$ where P is the Principal amount, r is the rate of interest, n is the number of periods in an year and t is the number of years.

Calculations: Plugging values P = 500, r = 4% = 0.04, n= 4 (for quarterly compound) and t=10 in above formula, we get

  $\begin{array}{l}A=500{\left(1+\frac{0.04}{4}\right)}^{4\cdot 10}\\ =500{\left(1+\frac{0.04}{4}\right)}^{40}\\ =500{\left(1+0.01\right)}^{40}\\ =500{\left(1.01\right)}^{40}\\ \approx 500(\text{1}\text{.48886})\\ \approx \text{744}\text{.43}\end{array}$

Therefore, the balance after 10 years is $\$\text{744}\text{.43}.$