# 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 $$\displaystyle{15}\%$$.

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

sovienesY
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.