The solution to this problem requires time value of money calculations.Reference to Tables 9-1 through 9-4 in the text is necessary to complete the calculations.
The total amount of interest compounded quarterly on a $2,000 note payable for 1 year at 8% is
A) $164.86
B) $240.00
C) $40.00
D) None of these choices.

Question

The solution to this problem requires time value of money calculations.Reference to Tables 9-1 through 9-4 in the text is necessary to complete the calculations. ​
The total amount of interest compounded quarterly on a $2,000 note payable for 1 year at 8% is
A) $164.86
B) $240.00
C) $40.00
D) None of these choices.

Quizplus · Accepted Answer

Using the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = total amount after t years
P = principal amount
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time in years

In this problem:
P = $2,000
r = 0.08
n = 4 (compounded quarterly)
t = 1 year

So, the formula becomes:
A = $2,000(1 + 0.08/4)^(4*1)
A = $2,000(1.02)^4
A = $2,168.32

The total amount of interest would be:
Total interest = A - P
Total interest = $2,168.32 - $2,000
Total interest = $168.32

However, we need to find the amount of interest compounded quarterly. To do this, we use Table 9-4 in the text, which gives the values of (1+r/n)^(n*t) for different values of n and t.

When n=4 and t=1, Table 9-4 gives the value of (1+r/n)^(n*t) as 1.02. This means that the amount of interest earned in each quarter is:

Interest per quarter = ($2,000 * 1.02) - $2,000
Interest per quarter = $40.00

Since there are 4 quarters in a year, the total amount of interest is:

Total interest = $40.00 * 4
Total interest = $160.00

Therefore, the answer is A) $164.86, which is the closest option to the calculated value.

The Solution to This Problem Requires Time Value of Money