Question

Payments of $700 due three months ago and $1000 six months from now are to be replaced by one equivalent payment four months from now. What is the size of this payment if money can earn 7%?

Answer 1

first let us know the current value of $700 due three months ago;

this can be known using future value formula => amount *(1+r)^n

amount = $700

r =7% for one year =>7%*3/12 =>1.75% for 3 months

n = one 3 month period =>1.

current value = $700*(1.0175) =>$712.25.

now,

present value of $1000 due in six months

=> amount / (1+r)^n

here,

amount = $1000

r= 7% * 6/12 =>3.5% for six months.

n = one six month period

=>1

present value = $1000/(1.035)

=>$966.18.

total current value of obligation =$712.25+966.18=>$1,678.43.

amount to be paid four months from now = current value *(1+r)^n

current value = $1678.43

r=7% *4/12 =>2.33%=>0.0233.

n= one 4 month period

so the equivalent payment = $1678.43*(1.0233)^1

=>$1,717.54.