Question 1155280: Della Riley borrowed $2400 for 6 months to invest in a business venture. If she agreed to pay 8% interest annually, how much will she be repaying?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 8% per year divided by 2 = 4% every 6 months.
she will be repaying 2400 * 1.04 = 2496.
if you are talking simple interest, the formula is i = p * r * n
if it's 8% per year, and you are dealing with simple interest for 6 months, then the formula becomes i = 2400 * .08 * .5 = 96.
you repay 2400 principal plus 96 interest = 2496.
if you are talking compound interest, then the formula is f = p * (1 + r) ^ n
if you are talking two compounding periods per year, then the interest rate per compounding period is .08 / 2 = .04 and the number of compounding periods is equal to 1.
in that case, the formula becomes 2400 * (1 + .04) ^ 1 = 2496.
if you are talking compound interest with one compound period per year, then the formula becomes f = 2400 * (1.08) ^ (1/2).
solve for f to get 2494.153163.
the difference between one compounding period per year and two compounding periods per year is that, with 2 compounding periods per year, the annual interest rate is divided by 2 to get the semi-annual interest rate and the number of semi-annual periods becomes 1, but with 1 compounding periods per year, the annual interest remains at 8% and the number of periods becomes 1/2.
in the formula of f = p * (1 + r) ^ n:
f = future value
p = present value
r = interest rate per time periods.
n = number of time periods.
the exponent in the formula is the number of time periods.
with semi-annual time periods, the exponent is 1 for 6 months.
with annual time periods, the exponent is 1/2 for 6 months.
with semi-annual time periods, the factor becomes 1.04 ^ 1.
with annual time periods, the factors becomes 1.08 ^ (1/2).
1.04 ^ 1 gets you a factor of 1.04.
1.08 ^ (1/2) gets you a factor of 1.039230485.
the difference in those two factors explains why the future value is different when dealing with semi-annual time period instead of annual time periods.
the bottom line is:
with simple interest, she repays 2496.
with semi-annual time periods, she repays 2496.
with annual time periods, she repays 2494.153163.
since i have no way of knowing what type of interest formula they want you to assume, i gave you all three that i know of.
sorry to confuse you, but it does make a difference.
Answer by ikleyn(52908)  (Show Source):
You can put this solution on YOUR website! .
From the context and by DEFAULT, the problem is about simple interest, with NO any doubts.
So, the solution is VERY simple.
The simple interest formula for the Future value is
FV = L*(1 + rt),
where FV is the amount to repay; L is the borrowed amount (the loan amount) and "r" is the annual interest as decimal; t is the time.
In your case L = 2400 dollars; r = 8% = 0.08 (as decimal) and t = 0.5 of a year (6 months).
Therefore,
FV = 2400*(1 + 0.08*0.5) = 2496.
ANSWER. In 6 months, Della Rilley must repay $2496.
Solved, explained, completed and calculated.
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To see many other similar solved problems on simple interest accounts, look into the lesson
- Simple interest percentage problems
in this site.
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