SOLUTION: Tebongo opened his savings account with a single deposit of R5000 at the beginning of June 2015. He then made 24 monthly deposits of R800 at the end of every month starting at the
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-> SOLUTION: Tebongo opened his savings account with a single deposit of R5000 at the beginning of June 2015. He then made 24 monthly deposits of R800 at the end of every month starting at the
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Question 1083094: Tebongo opened his savings account with a single deposit of R5000 at the beginning of June 2015. He then made 24 monthly deposits of R800 at the end of every month starting at the end of June 2015. The account earned interest at 15% p.a compounded monthly. Calculate amount that should be in his savings account immediately after he makes a last deposit. Answer by Theo(13342) (Show Source):
he then made 24 monthly deposits of 800 at the end of every month starting at the end of june, 2015.
the account earned interest rate of 15% per year compounded monthly.
the amount he had in the account should be the future value of 5000 for 24 months plus the future value of 24 end of month payments.
the interest rate would be 15% / 12 = 1.25% per month.
if you use a time value of money calculator such as the one found at https://arachnoid.com/finance/, then your in puts and outputs will be as shown below:
the first inputs and outputs correspond to finding the future value of 5000 invested for 24 months at 1.25% interest rate per month.
the future value of 5000 invested for 24 months at 1.5% interest rate per month is equal to 6,736.76.
the second inputs and outputs correspond to finding the future value of 800 invested at the end of each month for 24 months at 1.25% interest rate per month.
the future value of 800 invested at the end of each month for 24 months at 1.5% interest rate per month is equal to 22,230.47
add them up and the total value at the end of the 24 months is 28,967.23.
you can also look at the individual cash flows and then calculate the future value of all those cash flows.
i did this using excel and got the following results.
if you need to do this manually, you can use the formulas from the following referenced:
the formulas you would be interested in for this problem are:
FUTURE VALUE OF A PRESENT AMOUNT
f = p*(1+r)^n
f is the future value.
p is the present amount.
r is the interest rate per time period.
n is the number of time period.
and:
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
if you try to duplicate the formulas using your calculator, make sure you use the parentheses exactly as shown.
