Question

Nina invests a sum of money in a savings account with an

annual interest rate of 4.61% compounded continuously.
After 6 years, the balance reaches $5274.56. What
was the amount of the initial investment?

And I would like the formula to use please :)

Answer 1

The amount of the initial investment by Nina is $2271 approximately.

Solution:

Given, Nina invests a sum of money in a savings account with an annual interest rate of 4.61% compounded continuously.

After 6 years, the balance reaches $5274.56.

We have to find what was the amount of the initial investment?

We know that, compound interest is given as

`\text { Compound interest }=\text { amount } *\left(1+\frac{\text { interest rate }}{100}\right)^{\text {time period }}`

Now, balance = invested amount + compound interest.

`\begin{array}{l}{5274.56=\text { amount }+\text { amount } *\left(1+(4.61)/(100)\right)^(6)} \\\\ {5274.56=\text { amount }\left(1+\left(1+(4.61)/(100)\right)^(6)\right)} \\\\ {5274.56=\text { amount }\left(1+(1+0.0461)^(6)\right)} \\\\ {5274.56=\text { amount } * \left(1+1.0461^(6)\right)} \\\\ {5274.56=\text { amount } * (1+1.31050)} \\\\ {\text { Amount }=(5274.56)/(2.31050)=2271.1729}\end{array}`

Hence, the invested amount of money is $2271 approximately.