The amount required to be paid today. Given: The total amount in account after 5 years is $10000. The rate of compound interest of 15\%.

Caelan 2021-08-16 Answered
The amount required to be paid today.
Given: The total amount in account after 5 years is $10000.
The rate of compound interest of \(\displaystyle{15}\%\).

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Expert Answer

sovienesY
Answered 2021-08-17 Author has 10351 answers
Concept used:
Write the expression for the total amount in the account after some time.
\(\displaystyle{A}={P}{\left({e}^{{{r}\times{n}}}\right)}\) .....(I)
Here, the principal amount added in account is P, the rate of compount interest is r and time period is n.
Calculation:
Calculate the amount required to be paid today.
Substitute $10000 for A, \(\displaystyle{15}\%\) for r and 5 for n in Equation (I).
\(\displaystyle\${10000}={P}{\left({e}^{{{\left({0.15}\right)}{\left({5}\right)}}}\right)}\)
\(\displaystyle{P}={\frac{{\${10000}}}{{{\left({2.72}^{{{0.75}}}\right)}}}}\)
\(\displaystyle{P}={\frac{{\${10000}}}{{{2.117}}}}\)
\(\displaystyle{P}=\${4723.66}\)
The amount required to be paid today is $4724.
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