Question 1193492: Suppose 80,000 is due at the end of 4 years with interest at 10%
compounded quarterly. If money is worth 14% compounded quarterly,
what is the value of obligation,
a. Now,
b. At the end of 3 years, and
c. At the end of 6.5 years
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm not sure exactly what this means.
if i get it wrong, please explain how i should interpret this.
the statement is:
Suppose 80,000 is due at the end of 4 years with interest at 10%
compounded quarterly. If money is worth 14% compounded quarterly,
what is the value of obligation, .....
a. Now,
b. At the end of 3 years, and
c. At the end of 6.5 years
i believe what they're saying is that the cost of money is 14% per year compounded quarterly.
if so, that would be the discount rate for the problem.
as for the statement:
Suppose 80,000 is due at the end of 4 years with interest at 10%
compounded quarterly.
i'm assuming that the 80,000 is the present value of the loan and that the future value of the loan will be the present value times the loan interest rate for 4 years.
in other words, 80,000 * (1 + .10/4) ^ (4 * 4) is the future value.
that becomes 80000 * 1.025 ^ 16 which is equal to 118,760.45, rounded to the nearest penny.
the value of that today, at the cost of money of 14% per year, compounded quarterly will be:
118,760.45 / (1 + .14/4) ^ (4 * 4).
that becomes:
118,760.45 / 1.035 ^ 16 which is equal to 68,489.85.
what this means, in my opinion, is that:
if you invested 68,489.85 today at 14% compounded quarterly, then you would have enough to pay off the loan in 4 years.
the formula for that would be:
68,489.85 * 1.035 ^ 16 = 118,760.45.
68,489.85 is the present value.
1.035 is the growth factor per quarter.
16 is the number of quarters.
118,760.45 is the future value.
the growth factor is equal to 1 + the interest rate per quarter.
1.035 growth factor give you an interest rate of .035 per quarter.
multiply that by 4 and you get the nominal interest rate per year of .14, which is equal to 14%.
percent / 100 = rate
rate * 100 = percent.
bottom line, if i got this right:
future value of the loan at 10% per year compounded quarterly is equal to 118,760.45.
if you invest 68,489.85 today at 14% per year compounded quarterly, you will have 118,760.45 in 4 years.
68,489.85 is therefore the value of the loan today at 14% per year compounded quarterly.
let me know if you have any questions and if this answer was good for you.
if it is not, then it's because my assumptions were wrong.
in that case, please let me know what the assumptions for this problem should be and i'll provide you with a suitable solution based on those.
theo
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