Answer:
$52,651.14
Step-by-step explanation:
To determine how much money Pasha will have in his savings account at the end of 4 years, we can use the compound interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\\\\A=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]
In this case:
- P = $50,000
- r = 1.3% = 0.013
- n = 1 (annual)
- t = 4 years
Substitute the values into the formula and solve for A:
[tex]A=50000\left(1+\dfrac{0.013}{1}\right)^{1 \cdot 4}\\\\\\A=50000\left(1+0.013\right)^{4}\\\\\\A=50000\left(1.013\right)^{4}\\\\\\A=50000(1.053022816561)\\\\\\A=52651.14082805\\\\\\A=\$52,651.14\; \sf (nearest\;cent)[/tex]
Therefore, Pasha would have $52,651.14 in his savings account after 4 years.
