Caelan

2021-08-16

The amount required to be paid today.

Given: The total amount in account after 5 years is $10000.

The rate of compound interest of$15\mathrm{\%}$ .

Given: The total amount in account after 5 years is $10000.

The rate of compound interest of

sovienesY

Skilled2021-08-17Added 89 answers

Concept used:

Write the expression for the total amount in the account after some time.

$A=P\left({e}^{r\times n}\right)$ .....(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,$15\mathrm{\%}$ for r and 5 for n in Equation (I).

$\mathrm{\$}10000=P\left({e}^{\left(0.15\right)\left(5\right)}\right)}$

$P=\frac{\mathrm{\$}10000}{\left({2.72}^{0.75}\right)}}$

$P=\frac{\mathrm{\$}10000}{2.117}}$

$P=\mathrm{\$}4723.66}$

The amount required to be paid today is $4724.

Write the expression for the total amount in the account after some time.

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,

The amount required to be paid today is $4724.

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