Question

Find the value and interest earned if $8906.54 is invested for 9 years at % compounded a) semiannually b) continuosly

Modeling data distributions
ANSWERED
asked 2020-11-29
Find the value and interest earned if $8906.54 is invested for 9 years at \(\%\) compounded
a) semiannually
b) continuosly

Expert Answers (1)

2020-11-30
a) The future value for the amount $8906.54 for 9years at \(3\%\) compounded semiannually is calculated a follows.
\(\displaystyle{A}={P}{\left({1}+\frac{r}{{2}}\right)}^{2}{t}{\left(\text{semiannually}\right)}\)
\(\displaystyle{A}={8906.4}{\left({1}+\frac{0.03}{{2}}\right)}^{{{\left({2}\cdot{9}\right)}}}\)
\(\displaystyle=\${11643.88}\)
b) The future value for the amount $8906.54 for 9years at \(3\%\) compounded continuously is calculated a follows.
Future value \(\displaystyle={A}{e}^{r}{t}\)
\(\displaystyle={\left({8906.54}\right)}{e}^{{{\left({0.03}\right)}{\left({9}\right)}}}\)
\(\displaystyle=\${11667.25}\)
Interest earned \(\displaystyle={A}-{P}\)
\(\displaystyle={11667.25}-{8906.54}\)
\(\displaystyle=\${2760.71}\)
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