Respuesta :
The ending balance is 59,139.60
Here, we want to find the balance for a retirement account in which the initial deposit is compounded monthly at a certain percentage
Mathematically, we proceed to use the compound interest formula ;
[tex]\begin{gathered} A\text{ = P(1 + }\frac{r}{n})^{nt} \\ \\ \text{where A is the balance we want to calculate} \\ \\ P\text{ is the amount deposited which is 2,500} \\ \\ r\text{ is the annual interest rate which is 6.75\% which is 0.0675} \\ \\ n\text{ is the number of times the interest is componded yearly} \\ At\text{ a monthly rate, we have 12 times per year} \\ \\ t\text{ is the number of years which is 65-18 = 47} \end{gathered}[/tex]So, we proceed to insert these values;
[tex]\begin{gathered} A\text{ = 2500( 1 + }\frac{0.0675}{12})^{12\times47} \\ \\ A=2500(1+0.005625)^{564} \\ \\ A=2500(1.005625)^{564} \\ \\ A\text{ = 59,139.60} \end{gathered}[/tex]