Calculate the future value of quarterly payments of $1200 for 5 years, if the rate of interest was 10% compounded quarterly for the first 2 years and will be 9% compounded quarterly for the last 3 years.

I solved for both which i got

aFV= $10483.34
bFV= $16322.67
to get this answer i used this formula: FV=PMT((1+i)^n))-1/i

i just don't know what i should do now?

$10483.34 is the future value of the first two years of investment at the end of the second year.

$16322.67 is the future value of the 3rd, 4th and 5th years of investment at the end of the fifth year (end of term).

The only thing left to do is to calculate the future value of the first two years of investment at the end of term (5th year) at the rate of 9% pa, or 2.25% per quarter.
FV=10483.34*(1.0225)^(4 quarters * 3 years)
= 10483.34*(1.0225)^12
= $13691.76

So the total future value at end of term (5 years) is:
$13691.76+16322.67
=$30014.43

Check my work.

Thank u soo much...u really helped me at the right time...i have final exam tomorrow...and i am now prepared..thanks again!!!

To calculate the total future value of the quarterly payments, you need to consider two different interest rates and time periods.

For the first two years, where the interest rate is 10% compounded quarterly, you can use the formula for the future value of an ordinary annuity:

FV = PMT * ((1 + r)^n - 1) / r

Where:
PMT = $1200 (quarterly payment)
r = 0.10/4 (quarterly interest rate)
n = 4 * 2 (number of quarters in 2 years)

Substituting the values into the formula:

FV1 = $1200 * ((1 + 0.10/4)^(4 * 2) - 1) / (0.10/4)

FV1 = $1200 * (1.025)^8 - 1) / (0.025)

FV1 ≈ $4,978.09

Now, for the last three years, where the interest rate is 9% compounded quarterly, you need to calculate the future value of the remaining principal amount. The remaining principal amount is the initial principal minus the future value calculated for the first two years.

Principal remaining after 2 years:
Principal remaining = $1200 * ((1 + 0.10/4)^8 - 1) / (0.10/4)
Principal remaining ≈ $4,978.09

Now, calculate the future value for the remaining principal using a 9% interest rate:

FV2 = Principal remaining * ((1 + 0.09/4)^(4 * 3) - 1) / (0.09/4)

FV2 ≈ $4,983.25 * (1.0225)^12 - 1) / (0.0225)

FV2 ≈ $5,545.25

Finally, sum up the two future values calculated:

Total Future Value = FV1 + FV2
Total Future Value ≈ $4,978.09 + $5,545.25
Total Future Value ≈ $10,523.34

Therefore, the future value of the quarterly payments over 5 years would be approximately $10,523.34.