If business manager deposits $30,000 in a savings account at the end of each year for twenty years what will be the value of her investment at a compound rate of 12 percent? and at 18 percent?
Future value at 12%
=30000*1.12^20
=$289388.79
Similarly for 18%, but almost 3 times as much.
To calculate the future value of an investment at a compound interest rate, we can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r,
where:
FV = future value of the investment,
P = periodic deposit or payment,
r = interest rate per period, and
n = number of periods.
Given the information, we can calculate the future value of the investment for different interest rates.
For 12 percent interest rate:
P = $30,000 (the business manager's annual deposit)
r = 12% = 0.12 (converted to decimal)
n = 20 years
Plugging the values into the formula:
FV = $30,000 * ((1 + 0.12)^20 - 1) / 0.12
For 18 percent interest rate:
P = $30,000 (the business manager's annual deposit)
r = 18% = 0.18 (converted to decimal)
n = 20 years
Plugging the values into the formula:
FV = $30,000 * ((1 + 0.18)^20 - 1) / 0.18
To simplify the calculations, you can use a financial calculator, spreadsheet software, or an online compound interest calculator. These tools can easily calculate the future value based on the given inputs.