SOLUTION: Matt is saving to buy a new motorcycle. If he deposits ​$55 at the end of each month in an account that pays an annual interest rate of 3.5​%, how much will he have in

Algebra ->  Finance -> SOLUTION: Matt is saving to buy a new motorcycle. If he deposits ​$55 at the end of each month in an account that pays an annual interest rate of 3.5​%, how much will he have in       Log On


   

Question 1099777: Matt is saving to buy a new motorcycle. If he deposits ​$55 at the end of each month in an account that pays an annual interest rate of 3.5​%, how much will he have in 15 ​months? Assume that the compounding is being done monthly.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
he's depositing 55 at the end of each month.
the interest rate if 3.5% per year compounded monthly.
how much will he have in 15 months?

using a financial calcujlator, like the Texas Instruments BA II Plus, you would do the following:

PV = 0
FV = 0
AMT = -55
I/Y = 3.5% / 12 = .29166666.....
N = 15
set PMT to end of time period.

you would then compute FV to get FV = 842.0585111 which you can then round to 842.06.

that's now much he'll have at the end of 15 months.

you can also do this with an online calculator, such as the one found at https://arachnoid.com/finance/

you will get results that look like this:

$$$

your inputs are the same as with the TI BA II Plus calculator.

present value = 0
future value = 0
number of time periods = 15
interest rate percent per time period = .29166666666
amount = -55
payment set to end of time period

you then click on FV and the calculator tells you that the future value is equal to 849.06

you can also use a formula to do it manually using your own scientific calculator.

the one that i use is the Texas Instruments TI-84 Plus.

the formula you would use is shown below:

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

with this formula:

a = 55
r = .035 / 12 = .00291666667
n = 15
f = the future value that you want to find.

after making your entries, the formula will look like this:

f = (55*((1+.00291666667)^15-1))/.00291666667

you would then use your scientific calculator and enter the problem as shown.

the calculator will tell you that f = 842.0585122 which you can then round to 842.06.

a summary of financial formulas can be found at https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f3