FVoa = PMT[((1 + r)^n - 1) / r]
r = 0.08 / 4 qtrs per year = 0.02
n = 4 qtrs
FVoa = $500[(1.02^4) - 1 / 0.02]
= 500[1.08243 - 1 / 0.02]
= 500[0.08243 / 0.02]
= 500[4.12161]
= $2,060.08
Your deposits total $500 * 4 = $2,000
interest is 2060.80 - 2,000 = 60.80
Year two:
FV, at end year 2,of the balance at the end of year 1: 2060.80(1.02^4) = 2230.68
interest on this portion: 2230.68 - 2060.80 = $169.88
interest on the quarterly $500 payments (as above in first year): 60.80
Total interest year 2: 169.88 + 60.80 = $230.68
At the end of year 2 (with 4 $500 more pmts made) your balance is:
2230.68 + 2060.80 = 4291.48
Year 3: FV of the 4291.48 = 4291.48(1.02^4) = 4,645.24
interest on this portion: 4645.24 - 4291.48 = $353.76
interest on the third set of four $500 pmts (as above): 60.80
total interest year 3: 353.76 + 60.80 = 414.56
End balance: 4645.24 + 2060.80 = 6706.04
less (4 * 3 * $500) = 6000 in pmts = $706.04 in interest over the 3 years
check math - use the total time horizon of 3 years, n = 3 * 4 = 12
FVoa = $500[1.02^12) - 1) / 0.02]
= 500[(1.26824 - 1) / 0.02]
= 500{13.41209]
= $6,706.04
Voila!
You could do it long-hand (by hand or in excel**) or ...
Start with finding the future value of an ordinary annuity. The multi-step way would be to do it for yr 1 then yr 2 then yr 3. **You could also set up an excel spreadsheet to do the computations - and have it compute the yearly interest earned.
I feel your pain.
I can't seem to figure out how to solve this problem. please guide me through the steps.
Problem:
If $500 is deposited each quarter into an account paying 8% interest compounded quarterly for 3 years, find the interest earned during each of the 3 years.
the textbook says: year 1: $60.80
year 2: $230.68
year 3:$414.56
I just dont understand how they got this..
Thanks!
