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Suppose you want to have $800,000 for retirement in 30 years. Your account earns 8% interest.
a) How much would you need to deposit in the account each month?
$
b) How much interest will you earn?
$
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To be consistent, the condition should be edited in this way:
Suppose you want to have $800,000 for retirement in 30 years. Your account is compounded monthly and earns 8% annual interest.
Then the solution is THIS :
It is a classic Ordinary Annuity saving plan. The general formula is
FV = ,
where FV is the future value of the account; P is the monthly payment (deposit); r is the monthly percentage yield presented as a decimal;
n is the number of deposits (= the number of years multiplied by 12, in this case).
From this formula, you get for the monthly payment
P = . (1)
Under the given conditions, FV = $800,000; r = 0.08/12; n = 30*12. So, according to the formula (1), the monthly payment is
P = = $536.78.
Answer. a) How much would you need to deposit in the account each month ? - $536.78.
Note that of projected $800,000 the total you deposit will be only 30*12 times $536.78, i.e. about 30*12*536.78 = 193241 dollars.
The rest is what the account will earn/accumulate in 30 years.
b) How much interest will you earn ? - You will earn = 314% of interest.
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On Ordinary Annuity saving plans, see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
in this site.