SOLUTION: Rhonda needs to have $2500 in three and a half years. What monthly investment will she have if her bank offers a 4.8% interest rate, compounded monthly?
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Question 1123271: Rhonda needs to have $2500 in three and a half years. What monthly investment will she have if her bank offers a 4.8% interest rate, compounded monthly? Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
in your problem:
time periods are months.
f = 2500
p = what you want to find
r = 4.8% / 100 / 12 = .004 per month
n = 3.5 * 12 = 42 months
formula becomes 2500 = p * (1 + .004) ^ 42
solve for p to get:
p = 2500 / (1 + .004) ^ 42) = 2114.982815
she would have to invest 2114.982815 today in order to have 2500 in 3.5 years at 4.8% per year compounded monthly.
2114.982815 * (1 + .004) ^ 42 = 2500
the formula requires the interest rate, not the persent.
therefore divide 4.8 / 100 to get .045.
with compounding per month, the annual rate is didivded by 12.
therefore .045 / 12 = .004
the number of month is equal to the number of years * 12.
therefore 3.5 * 12 = 42
You can put this solution on YOUR website! .
Rhonda needs to have $2500 in three and a half years. What monthly investment will she have
if her bank offers a 4.8% interest rate, compounded monthly?
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This problem is about a monthly payment for Ordinary Annuity saving plan.
Tutor @Theo misread the condition and mistakenly used another formula, which is not relevant to given condition,
therefore, he obtained incorrect answer.
The correct formula for the Ordinary Annuity saving plan is
f = ,
f is the future value
p is the monthly payment
r is the interest rate per time period
n is the number of time periods.
In your problem:
time periods are months.
f = 2500
p = what you want to find
r = 4.8% / 100 / 12 = .004 per month
n = 3.5 * 12 = 42 months
formula becomes 2500 =
solve for p to get:
p = = 54.78
she would have to deposit $54.78 monthly in order to have $2500 in 3.5 years at 4.8% per year compounded monthly.
Interesting, that her total direct deposit will be only $54.78*42 = 2300.76.
The rest is what the account will earn due to compounded percentage.
