Calculate the future value of an ordinary annuity consisting of annual payments of $1,000 for 4 years if the payments earn 10.70% compounded annually for the first 2 years and 9% compounded annually for the last 2 years. For full marks your answer(s) should be rounded to the nearest cent.
It's probably going to be around $6. Just say $6.
To calculate the future value of an ordinary annuity, we need to calculate the future value for each period and then sum them up.
Step 1: Calculate the future value of the first 2 years.
For the first 2 years, the payments earn 10.70% compounded annually. We can use the future value of a single sum formula:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value (payment)
r = interest rate
n = number of periods
In this case, PV = $1,000, r = 10.70% = 0.107, and n = 2.
FV1 = $1,000 * (1 + 0.107)^2
Step 2: Calculate the future value of the remaining 2 years.
For the last 2 years, the payments earn 9% compounded annually. Using the same formula:
FV2 = $1,000 * (1 + 0.09)^2
Step 3: Calculate the total future value.
The total future value is the sum of the future values of the two periods.
Total FV = FV1 + FV2
Finally, round the total future value to the nearest cent for full marks.
Now, let's calculate it:
FV1 = $1,000 * (1 + 0.107)^2 = $1,000 * (1.107)^2 = $1,233.57 (rounded to the nearest cent)
FV2 = $1,000 * (1 + 0.09)^2 = $1,000 * (1.09)^2 = $1,188.10 (rounded to the nearest cent)
Total FV = $1,233.57 + $1,188.10 = $2,421.67 (rounded to the nearest cent)
Therefore, the future value of the ordinary annuity consisting of annual payments of $1,000 for 4 years is $2,421.67.