You have $30000 to invest. write the expression to find the total value of the investment if: a) you invest at 6% interest for 7 years compounded quar

Nann 2021-05-28 Answered
You have $30000 to invest. write the expression to find the total value of the investment if: a) you invest at 6% interest for 7 years compounded quarterly b) you invest for 7 years compounded continuously.

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Gennenzip
Answered 2021-05-29 Author has 22238 answers
Use the compound interest formula: \(\displaystyle{A}={P}{\left({1}+\frac{{r}}{{n}}\right)}^{{n}}{t}\) where A is the final value, P is the present value, r is the rate (in decimal form), and n is compounding times per year, and t is the time in years.
Substitute P=3000, r=0.06 (for 6%), n=4, and t=7: \(\displaystyle{A}={3000}{\left({1}+\frac{{0.06}}{{4}}\right)}^{{4}}{\left({7}\right)}\)
\(\displaystyle{A}={3000}{\left({1.015}\right)}^{{28}}\)
A ~ $4551.67
Use the continuos compounding interest formula: \(\displaystyle{A}={P}{c}^{{r}}{t}\)
where A is the final value, P is the present value, r is the rate (in decimal form), and t is the time in years.
Substitute P=3000, r=0.06 (for 6%), and t=7: \(\displaystyle{A}={3000}{c}^{{{0.06}}}{\left({7}\right)}\)
\(\displaystyle{A}={3000}{c}^{{0.42}}\)
A ~ $4365.88
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