SOLUTION: You want to purchase a new car in 3 years and expect the cost to be $15000. Your bank offers a savings plan with an annual interest rate of 5.5% if you make regular monthly deposi

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Question 1103194: You want to purchase a new car in 3 years and expect the cost to be $15000. Your bank offers a savings plan with an annual interest rate of 5.5% if you make regular monthly deposits. How much should your monthly deposits be in order to end up with $15000 in 3 years? Round your answer to the nearest cent.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the monthly payments need to be 384.1885271 dollars.
round to nearest penny = 384.19.

i used the texas instruments business analyst II.

you can also use an online financial calcujlator.

one that i use is at https://arachnoid.com/finance/

the result of my session is shown below:

i entered:

present value = 0
future value = -15000
number of time periods = 3 years * 12 months per year = 36 months.
payment amount was left blank.
interest rate per time period = 5.5% / 12 = .4583333%
payment made at end of time period.

i then clicked on PMT and it told me that the monthly payment needed to be $384.19.

you can also solve by formula.

the formula you need is:

ANNUITY FOR A FUTURE AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (f*r)/((1+r)^n-1)
a is the annuity.
f is the future amount.
r is the interest rate per time period.
n is the number of time periods.

a is what you're looking for.
f is 15000
r is 5.5/1200
n is 3*12

formula becomes a = (15000*5.5/1200)/((1+5.5/1200)^36-1)

stick that in your calculator exactly as shown and you will get a = 384.1885... which rounds to 384.19.

the interest rate of 5.5/1200 is 5.5% / 100 = .055 / 12 = .00458333333.....

that's your monthly interest rate.

3*12 is your number of months.