Question

Sam deposits $2,500.00 into a retirement annuity at the age of 18 and plans to withdraw the money for retirment at the age of 65. The annuity Interest rate is 6.75% interest, compounded monthly. What is the ending balance?

Answer 1

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 ;

`\begin{gathered} A\text{ = P(1 + }(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}`

So, we proceed to insert these values;

`\begin{gathered} A\text{ = 2500( 1 + }(0.0675)/(12))^(12*47) \\ \\ A=2500(1+0.005625)^(564) \\ \\ A=2500(1.005625)^(564) \\ \\ A\text{ = 59,139.60} \end{gathered}`