Question 1190272: Suppose you want to have $700,000 for retirement in 30 years. Your account earns 7% interest.
a) How much would you need to deposit in the account each month? (Round up to the dollar's place.)
b) How much interest will you earn?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (a)
Future value of annuity formula
FV = P*( (1+i)^n - 1 )/i
where,
FV = future value
P = periodic deposit
i = interest rate per period
n = number of periods
In this case,
FV = 700,000
P = unknown monthly deposit
i = 0.07/12 = monthly interest rate
n = 12*30 = 360 months
Let's plug in the values mentioned and solve for P
FV = P*( (1+i)^n - 1 )/i
700,000 = P*( (1+0.07/12)^360 - 1 )/(0.07/12)
700,000 = P*1,219.97099577594
P = (700,000)/(1,219.97099577594)
P = 573.784132920946
P = 573.78
You need to deposit $573.78 per month, for 360 months, so that you end up with a future value of about $700,000.
Your teacher then states to round up to the nearest dollar. So we go from 573.78 to 574
Answer: $574
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Part (b)
If you plugged P = 574, i = 0.07/12, and n = 360 into the future value annuity formula, then you'd get roughly FV = 700,263.35
We don't hit $700,000 exactly, but instead go over a bit.
The alternative is that if P = 573, then FV would be somewhat shy of the 700 thousand dollar goal.
So this is why we rounded up.
Ignore the interest portion for now.
If you made 360 deposits of $574 each, then you paid 360*574 = 206,640 dollars into the account.
The total interest is the difference of the results we got
700,263.35 - 206,640 = 493,623.35
Answer: $493,623.35
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