Question

Two debts, the first of $1200 due nine months ago and the second of $1000 borrowed one year ago for a term of four years at 9.4% compounded annually, are to be replaced by a single payment one year from now. Determine the size of the replacement payment if interest is 8.5% compounded quarterly and the focal date is one year from now The size of the replacement payment is $0 (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

Answers :-

Size of the replacement payment is $2,982.17

.

Explanations :-

$1200 ---> due 8 months ago

$1000 ---> due 2 years ago

t = 4 years

j = 9.4% = 0.094

m = 1

i = 0.094

..

Single payment one year from now.

j = 8.5% = 0.085

m = 4

i = j/m = 0.085/4 = 0.02125

n = tm = 1(4) = 4

..

Sum of obligations = single payment

.

Compare the time of the debts by the focal date that is one year from now.

$1200 will have interest for 1.25 years

$1000 will have interest for 3 years

(1200(1.094)​^1.25)​​ + (1000(1.094)​^3)​​=x(1.02125)​^4

(1200 × 1.11884945) + (1000 × 1.3093386) =x 1.087747962

$1342.61934 + $1309..3386 =x(1.087747962) ,

$2651.95794= x(1.087747962)

X = $2651.95794 / 1.087747962

x = $2438.026

Size of the replacement payment is $2,982.17