How many compounding periods does it take for a non-interest bearing bond of $420 150 to be reduced to $199 989 at a discount rate of 5.44% compounded monthly?
A) 146.12
B) 121.12
C) 154.12
D) 184.12
E) 164.12

Question

Quizplus · Accepted Answer

To find the number of compounding periods, we can use the formula for the present value of a single sum, which is $PV = FV / (1 + r)^n$, where PV is the present value, FV is the future value, r is the monthly interest rate, and n is the number of compounding periods. Rearranging the formula to solve for n gives us $n = \log(PV/FV) / \log(1 + r)$. Given that the present value (PV) is $199,989, the future value (FV) is $420,150, and the annual discount rate is 5.44% (which gives a monthly rate of $5.44\% / 12 = 0.00453$ or 0.00453 when expressed as a decimal), we can substitute these values into the formula: $n = \log(199989/420150) / \log(1 + 0.00453)$. Calculating this gives us approximately 164.12 periods.

How Many Compounding Periods Does It Take for a Non-Interest