$25000 is invested for 4 years 9 months .If the invesment is offered 12% compounded semi anually for the first 2 years and 10% compounded quarterly for the rest of the period,find the future value of this invesment.
25000 * (1+.12/2)^(2*2) * (1+.10/4)^(4*2.75) = ?
To find the future value of the investment, we will calculate the value of each compounding period separately and then add them together.
First, we'll calculate the value of the investment for the first two years at a 12% annual interest rate compounded semi-annually.
Step 1: Convert the annual interest rate to a semi-annual rate.
12% divided by 2 = 6% semi-annual interest rate.
Step 2: Determine the number of compounding periods.
There are 2 years, which is equal to 4 semi-annual periods (2 periods per year).
Step 3: Calculate the future value for the first two years.
Future Value = Principal * (1 + (Interest Rate per Period))^Number of Periods
Future Value = $25000 * (1 + 6%/100)^4
Future Value = $25000 * (1 + 0.06)^4
Future Value = $25000 * (1.06)^4
Future Value = $25000 * 1.262476 = $31561.90 (rounded to the nearest cent)
The future value of the investment after the first two years is $31561.90.
Next, we'll calculate the value of the investment for the remaining period of 2 years and 9 months at a 10% annual interest rate compounded quarterly.
Step 4: Convert the annual interest rate to a quarterly rate.
10% divided by 4 = 2.5% quarterly interest rate.
Step 5: Determine the number of compounding periods.
There are 2 years and 9 months, which is equal to 11 quarterly periods (4 periods per year).
Step 6: Calculate the future value for the remaining period.
Future Value = Principal * (1 + (Interest Rate per Period))^Number of Periods
Future Value = $31561.90 * (1 + 2.5%/100)^11
Future Value = $31561.90 * (1 + 0.025)^11
Future Value = $31561.90 * (1.025)^11
Future Value = $31561.90 * 1.303836 = $41113.51 (rounded to the nearest cent)
The future value of the investment for the remaining period is $41113.51.
Finally, we'll add the two future values together to find the total future value of the investment.
Total Future Value = Future Value for the first two years + Future Value for the remaining period
Total Future Value = $31561.90 + $41113.51
Total Future Value = $72675.41
Therefore, the future value of the investment after 4 years and 9 months is $72675.41.