Question

Find the present value of$5436.22 due in four years and three months at 4% compounded annually. a:$4601.56 b:$4592.55 c:$4646.90 d:$6422.27

Upper Level Math
ANSWERED
asked 2020-12-28
Find the present value of$5436.22 due in four years and three months at 4% compounded annually.
a:$4601.56
b:$4592.55
c:$4646.90
d:$6422.27

Answers (1)

2020-12-29

Given:
Principle amount \((p):=$5436.22\)
Interest rate\((r)=4\%=\)\(\frac{4}{100}\)\(=0.04\)
interest time \((t)=4\) years 3 months
number of times interest compounded per year(n)=1(given annually compounded)
present value \((A)=?\)
Steps:
Formula for compound interest
\(A=P(1+\frac{r}{n})^{nt}\)
\(\Rightarrow A=5436.22(1+(\frac{0.04}{1})^{1 \cdot 4.25})\)
\(=5436.22(1+0.04)^{4.25}\)
\(=5436.22(1.04)^{4.25}\)
\(A=5436.22(1.181386)\)
\(A=$6422.27\)
present value \((A)=$6422.27\)
option d is the right answer

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