Question

Determine the proceeds of a non-interest-bearing note with a maturity value of $9,000 three years and ten months before the due date if the interest rate is 7% compounded semi-annually.

Select one: a. $6,900.44 b. $6,910.78 c. $6,911.58 d. $6,913.53

Answer 1

Answer:

Answer d) $6,913.53

Step-by-step explanation:

Hi, we have to bring the maturity value to present value, that is 3 years and 10 months before its due date (46 months, since 3 years +10 months is 46 months).

ok, in order to come up with the simplest solution to this problem, we have to turn this interest rate (7% compounded semi-annually) into an effective monthly rate. That is as follows.

$Effective-Semi-annual=\frac{0.07}{2} =0.035$

$Effective-Monthly=(1+0.035)^{(1/6)}-1=0.00575$

In other words, our discount rate is 0.575%

Now, we take it to present value using the following formula.

$PV=\frac{FV}{(1+r)^{n} }$

$PV=\frac{9000}{(1+0.00575)^{46} } =6,913.53$

Best of luck.