Answer:
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
[tex]\text { Compound interest }=\text { amount } \times\left(1+\frac{\text { interest rate }}{100}\right)^{\text {time period }}[/tex]
Now, balance = invested amount + compound interest.
[tex]\begin{array}{l}{5274.56=\text { amount }+\text { amount } \times\left(1+\frac{4.61}{100}\right)^{6}} \\\\ {5274.56=\text { amount }\left(1+\left(1+\frac{4.61}{100}\right)^{6}\right)} \\\\ {5274.56=\text { amount }\left(1+(1+0.0461)^{6}\right)} \\\\ {5274.56=\text { amount } \times \left(1+1.0461^{6}\right)} \\\\ {5274.56=\text { amount } \times (1+1.31050)} \\\\ {\text { Amount }=\frac{5274.56}{2.31050}=2271.1729}\end{array}[/tex]
Hence, the invested amount of money is $2271 approximately.