Question

Q1: Find the effective annual rate of interest (as a %, 2 decimal places) at which an amount of $2,000 today will accumulate to $6000 in 8 years.
(Solve using excel =RATE function; Answer in percentage rounded to two decimals without the % sign e.g. 1.8891 is 1.89)

Q2:

Which of the following is CORRECT? When discounting an amount to be received in one years' time at a rate that is quoted as 12% compounding quarterly, we can:

Select one:

A. Discount the amount using an effective monthly rate of 1% where the number of periods is 12.

B. Discount the amount using an effective annual rate (EAR) of (1+0.01)^12-1 =12.6825% where number of periods is 1.

C. Discount the amount using the annual rate of 12% where number of periods is 1.

D. Discount the amount using the effective quarterly rate of 3% where the number of discount periods is 4.

Answer 1

1.Effective annual rate can be calculated as under

(Future value/present value)^(1/year) -1 = (6000/2000)^(1/8) -1 = 14.72%

Using =RATE function of excel it can be found as under

=RATE(nper,pmt,pv,fv)

Where nper is number of periods which is 8 years, pmt is periodic payment which is 0 here, pv is present value which is -2000 here. Negative sign indicates that this cash out flow is required to get 6000 as cash inflow in future. FV is future value which is 6000 here.

=RATE (8,0,-2000,6000) = 14.72%

Thus, the asnwer is 14.72.

2. 12% compounded quarterly means per quarter the effective rate would be 12/4 = 3%. Division by 4 was done as there are 4 quarters in a year.

X% compounded semi annual would mean similarly that 6 months effective rate is X/2% as there are 2 6-month periods in a year.

A. Is wrong. Had it been stated that 12% compounded monthly, then it would have bee correct.

B. Is wrong. If 12%compounded monthly was there, then effective annual rate would be as described in this option.

C. Is wrong. As compounding is quarterly, annual effective rate is not 12% and period is not one.

D. Is correct. As explained above

Thus, answer is D.