Question

1, Janie Christopher lent $6000 to a friend for 90 days at 4.5% on November 5 2010, On December 5, 2010 she (a) Calculate the maturity value of the note (b) What interest rate did the third party receive? (No grace period among friends) sold this promissory note to a third party for $6000

Answer 1

(a)

The maturity value is the future value of $ 6,000 at an interest rate of 4.5% per year taken over a 3 month period. The formula to calculate future value is as follows:

$Future\:value=Present \:value(1+interest \:rate)^{period}$

Please note that in this case, both period and interest rate are going to be adjusted for a 3 month period. Substituting the values, we have

$Future\:value=6,000(1+\frac{0.045}{12}*3)^{\frac{3}{12}}$

Future value = 6,016.8

(b)

In this case, present value is $ 6,000 and future value is the maturity value which is $ 6,016.8. The period remaining is 2 months. Using the same equation used above we can calculate the interest rate as:

$6,016.8=6,000(1+\frac{interest\:rate}{12}*2)^{\frac{2}{12}}$

or interest rate = 10.15%