Answer to Question #138143 in Finance for CH Tan

Question #138143
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?
1
Expert's answer
2020-10-15T02:53:29-0400

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

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