Question

QUESTION 21 Jason manually calculated the present value of $500,000 at 4 percent 20 years from now to be $226,445.21 when interest is compounded semiannually. If Jason used the notation in the formula below to arrive at his answer, what is the numerical value of t in his formula? FV PV (1+r) O 10 O 20 O 40 120 O 200

Answer 1

Solution :

The formula given in the question is

PV = FV / ( 1 + r ) ^t

Where

PV = Present value ; FV = Future Value ; r = rate of interest ; t = Total Number of compounding periods ;

As per the information given in the question we have

FV = $ 500,000 ; PV = 226,445.21 ; r = 4 percent ;

Number of years = 20 years ; Number of compounding periods in a year = 2 ( since compounding is semi annual ) ;

We know that

t = Total Number of compounding periods = Number of years * Number of compounding periods in a year

= 20 years * 2 = 40 years ;

Thus the numerical value of 't' in the formula = 40.

The solution is option 3 = 40.