Questions: Suppose that you earned a bachelor's degree and now you're reaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit 2500 at the end of each year in an annuity that pays 6.25% compounded annually. a. How much will you have saved at the end of 5 years? b. Find the earnings on the investment.

Suppose that you earned a bachelor's degree and now you're reaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit 2500 at the end of each year in an annuity that pays 6.25% compounded annually.
a. How much will you have saved at the end of 5 years?
b. Find the earnings on the investment.

Transcript text: Suppose that you earned a bachelor's degree and now you're reaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $2500 at the end of each year in an annuity that pays 6.25% compounded annually. a. How much will you have saved at the end of 5 years? b. Find the earnings on the investment.

Solution

Solution Steps

Step 1: Calculate the Future Value (FV) of the annuity

The future value of an annuity can be calculated using the formula: $$ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) $$ Substituting the given values: $P = 2500$, $r = 0.0625$, and $n = 5$, we get: $$ FV = 2500 \times \left( \frac{(1 + 0.0625)^5 - 1}{0.0625} \right) = 14163.25 $$

Step 2: Calculate the Total Interest Earned

The total interest earned can be calculated by subtracting the total amount deposited from the future value of the annuity. $$ \text{{Total Interest}} = FV - (P \times n) $$ Substituting the calculated future value and given values: $FV = 14163.25$, $P = 2500$, and $n = 5$, we get: $$ \text{Total Interest} = 14163.25 - (2500 \times 5) = 1663.25 $$