diane works at a public university and contributes $625 per month in her retirement fund. the fund returns 3.84% a year, compounded monthly. how much will she have in her account after 15 years.
b. the economy gets better and the return is 7.72%. So now she contributes $1000 per month to the fund. how much will account be worth at the end of the next 15 years?
To calculate the future value of Diane's retirement fund after 15 years, we can use the formula for compound interest:
Future Value = P * (1 + r/n)^(n*t)
Where:
P = Monthly contribution
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Let's calculate the answers to both parts of the question:
a. Diane contributes $625 per month, and the fund returns 3.84% per year, compounded monthly. Therefore, we have the following values:
P = $625
r = 3.84% (or 0.0384 as a decimal)
n = 12 (compounded monthly)
t = 15 years
Plugging in these values into the formula:
Future Value = 625 * (1 + 0.0384/12)^(12*15)
Future Value = 625 * (1 + 0.0032)^(180)
Future Value = 625 * (1.0032)^(180)
Future Value ≈ $12,007.52
Therefore, Diane will have approximately $12,007.52 in her account after 15 years.
b. Now, Diane contributes $1000 per month, and the fund returns 7.72% per year. Using the same formula:
P = $1000
r = 7.72% (or 0.0772 as a decimal)
For this part, there is no mention of how frequently the interest is compounded. Assuming it remains monthly, we'll use n = 12 as before.
t = 15 years
Plugging in the values:
Future Value = 1000 * (1 + 0.0772/12)^(12*15)
Future Value = 1000 * (1 + 0.00643)^(180)
Future Value = 1000 * (1.00643)^(180)
Future Value ≈ $67,874.98
Therefore, Diane's retirement account will be worth approximately $67,874.98 at the end of the next 15 years.
Note: It's important to consider that these calculations assume consistent monthly contributions and a fixed interest rate. Market conditions and factors might affect the actual returns.