Problem 1
It's not clear if the person deposits at the start of the quarter, or at the end of the quarter. I'm going to assume they deposit at the end of the quarter. This means we go with an ordinary future value of annuity.
The formula we use is
F = P*( (1+i)^n - 1)/i
where,
- F = future value of the account
- P = payment per period
- i = interest rate per period
- n = number of periods
In this case,
- F = 300,000
- P = unknown, what we want to solve for
- i = 0.08/4 = 0.02
- n = 25*4 = 100 quarters (equivalent to 25 years)
So,
F = P*( (1+i)^n - 1)/i
300,000 = P*( (1+0.02)^100 - 1)/0.02
300,000 = P*(312.232305912618)
P = (300,000)/(312.232305912618)
P = 960.823061288088
P = 960.82
You must deposit $960.82 per quarter
If you deposit that amount of money per quarter, for 100 quarters, then you deposited a total of 960.82*100 = 96,082 dollars in total.
The amount of interest is 300,000 - 96,082 = 203,918 dollars
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Problem 2
We use the same formula from problem 1. This time we know the periodic payment ($250 per month) and we want to find the value of F
More specifically, we have this given info:
- P = 250
- i = 0.072/12 = 0.006
- n = 30*12 = 360 months (aka 30 years)
So,
F = P*( (1+i)^n - 1)/i
F = 250*( (1+0.006)^360 - 1)/0.006
F = 317,306.360545277
F = 317,306.36
If you deposit $250 per month, for 360 months, then you'll have $317,306.36 in the account.
This includes interest. The total amount deposited, without interest involved, is 250*360 = 90,000 dollars.
Therefore, the amount of interest earned is 317,306.36 - 90,000 = 227,306.36 dollars.
