Question

A finanical obligation requires the payments of $1000 in 2 months, $3000 in 8 months, and $4000 in 14 months. Instead, if a payment of $2000 is made now, when should a second payment of $6000 be made if interest is 9% compounded monthly?

Answer 1

For determining the second payment of $6000, if $2000 payment made today, we have to calculate the PV of first alternative series payment

Formula used PV = Fv x (1+r)^-n, here r = .09/12, n = 2/8/14, FV = 1000/3000/4000

PV of first alternative = 1000 x (1+.09/12)^-2 + 3000 x (1+.09/12)^-8 + 4000 x (1+.09/12)^-14

PV of first alternative =$985.17 + $2,825.93 + $3,602.71 => $7,413.80

In second alternative since $2,000 is already made today balance PV ($7413.80-$2,000) = $5,413.80

Now we have to calculate the n so that this sum of $5413.80 become $6000 at .09/12 rate

Formula used FV = PV x (1+r)^n, Here FV = 6000, PV = 5413.80, r = .09/12, n =?

Putting values in formula,

6000 = 5413.80 x (1+.09/12)^n

1.0075^n = 6000/5413.80

1.0075^n = 1.10827884

Taking ln both sides

N = Ln(1.10827884) / Ln(1.0075)

N = 13.7591 months, so next $6000 payment should be made after 13 month approx.