|A) 1389||B) 1359|
|C) 1379||D) 1339.33|
Given:j=7% compounded semiannually making m=2 and i = j/m= 7%/2 = 3.5%
Let x represent the third payment. Then the second payment must be 2x.
PV1,PV2, andPV3 represent the present values of the first, second, and third payments.
Since the sum of the present values of all payments equals the original loan, then
PV1 + PV2 +PV3 =$4000 -------(1)
PV1 =FV/(1 + i)^n =$1000/(1.035)^4= $871.44
At first, we may be stumped as to how to proceed for
PV2 and PV3. Let’s think about the third payment of x dollars. We can compute the present value of just $1 from the x dollars
PV2 =2x * 0.7089188 = 1.6270013x
PV3 =x * 0.7089188=0.7089188x
Now substitute these values into equation ➀ and solve for x.
$871.442 + 1.6270013x + 0.7089188x =$4000
Kramer’s second payment will be 2($1339.326) =$2678.65, and the third payment will be $1339.33