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Question 1161788: Ali wishes to replace payments of $1000 due today and $1300 due in 22 months by a single equivalent payment 18 months from now. If money is worth 3.8% compounded monthly, what should that payment be?
Interim calculations to 3 decimals, final answer rounded to the nearest cent.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the yearly interest rate is equal to 3.8% per year compounded monthly.
the monthly interest rate is therefore (3.8/12)% = .038/12.
the formula for future value to use is f = p * (1 + r) ^ n
the formula for present value to use is p = f / (1 + r) ^ n
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, which, in this case, are months.
1000 due today will cost you 1000 dollars in today's money.
1300 due 22 months from now will cost you p = 1300 / (1 + .038/12) ^ 22 = 1212.649543 in today's money.
what this means is that, if you invest that amount of money today at 3.8% compounded monthly, it will be worth f = 1212.649543 * (1 + .083/12) ^ 22 = 1300 in 22 months.
so, if you were to pay both of them today, they would cost you 1000 + 1212.649543 = 2212.649543 dollars.
if you pay that same amount of money 18 months from now, it will cost you f = 2212.649543 * (1 + .038/12) ^ 18 = 2342.223346 at that time.
round that to the nearest penny and you will have to pay 2342.22 eighteen months from now.
i did not round the intermediate results to 3 decimal places because i didn't have to.
the calculator i used stores the intermediate results rounded to the number of digits it is able to display, which is more than 3 decimal places.
if i had rounded the intermediate results, i would have gotten the following:
1000 due today is equal to 1000 today.
1300 due 22 months from now is equal to 1212.65 due today rounded to 3 decimal places.
their sum is 2212.65 today, rounded to 3 decimal places.
that sum * (1 + .038/12) ^ 18 is equal to 2342.22 eighteen months from now, rounded to 2 decimal laces.
either way i got 2342.22 in 18 months, rounded to 2 decimal places.
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