Question

Assume that your friend purchase a 6-year, 8 percent savings certificate for $1,000. If
interest is compounded annually, what will be the value of the certificate when it matures?
What is the difference between the ending value of the savings certificate compounded
semi-annually and the one compounded annually?

Answer 1

solution

Compounded annually

Principal $P= 1000$

Rate $r=0.08$

Period $n = 6$

$$A = P (1+r)^n$$ $$1000 (1.08)^6 = 1586.8743$$

answer: $ 1,586.8743

When compounding semi annually

Rate, $r=\frac{0.08}{2}=0.04$

Period, $n=6*2=12$

$$A=1000 (1.04)^{12}= 1601.0322$$

Difference between semi annual and annual compounding:

$1601.0322-1586.8743 = 14.1579$

answer: when compounding semi annually, the accumulated amount exceeds the amount compounded annually by $ 14.1579