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mike wants to save 20.000 for a motorcycle.
determine his monthly payment required if the bank offers a three year investment at 4,9% per year, compounded monthly.
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I will assume that Mike deposits a certain amount at the end of each month during three years.
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 = $280,000; r = 0.049/12; n = 3*12. So, according to the formula (1), you get for the monthly payment
P = = $516.86 (rounded to the nearest greatest cent).
Answer. The necessary monthly deposit value is $516.86.
Note that of projected $20,000, the total of Mike's deposits will be only 3*12 times $516.86, i.e. about 3*12*516.86 = 18606.96 dollars.
The rest is what the account will earn/accumulate in 3 years.
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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.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.
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Side note : your 4,9% from the condition I read as " 4.9% ".
Fix it in your post !