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 do i do now?
See answer to repost:
http://www.jiskha.com/display.cgi?id=1271904679
At the end of the first 2 years, the value of the payments up to that point will be
1200 ( 1.025^8 - 1)/.025 = 10483.339 (you had that)
let's "move" that up to the end of 5 years at the new rate
value = 10483.339(1.0225^12) = 13691.765
Amount of the last 3 years' payments at year 5
= 1200( 1.0225^12 - 1)/.0225 = 16322.666
so total amount = 16322.666 + 13691.765 = $30 014.43
Damon, didn't see that you already did this question.
Well, at least we agree down to the last penny, lol
Thank u soo much...u both really helped me at the right time...i have final exam tomorrow...and i am now prepared..thanks again!!!
To calculate the future value of quarterly payments with different interest rates over multiple periods, we can break the problem into two parts: calculating the future value of payments for the first two years at a 10% interest rate, and then calculating the future value of payments for the remaining three years at a 9% interest rate.
Step 1: Calculate the future value of payments for the first two years at a 10% interest rate.
First, we need to determine the number of payment periods for the first two years. Since the payments are made quarterly, there are 4 quarters in a year, so the number of payment periods would be 4 x 2 = 8.
To calculate the future value (FV) of quarterly payments, we can use the formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = future value of payments
P = quarterly payment amount
r = interest rate per period
n = number of payment periods
In this case, P = $1200, r = 10% per quarter (0.10), and n = 8.
Using the formula, we can calculate the future value of payments for the first two years:
FV1 = $1200 * ((1 + 0.10)^8 - 1) / 0.10
FV1 ≈ $12,096.52
Step 2: Calculate the future value of payments for the remaining three years at a 9% interest rate.
Following a similar approach, we can calculate the future value of payments for the remaining three years.
Using the same formula with the updated interest rate (9%), the number of payment periods would be 4 x 3 = 12.
In this case, P = $1200, r = 9% per quarter (0.09), and n = 12.
FV2 = $1200 * ((1 + 0.09)^12 - 1) / 0.09
FV2 ≈ $19,189.87
Step 3: Calculate the total future value by summing up the future values from the first and second steps:
Total Future Value = FV1 + FV2
Total Future Value ≈ $12,096.52 + $19,189.87
Total Future Value ≈ $31,286.39
Therefore, the future value of the quarterly payments of $1200 for 5 years, with a rate of interest of 10% for the first 2 years and 9% for the last 3 years, is approximately $31,286.39.