Question

You plan on going on a 11 month vacation 9 months from now. You can pay $4,118 per month during the vacation, or you can pay $33,934 today. If you pay today, how much does it save (or cost) you in present value term if your investments earn 4.85% APR (compounded monthly)? If it costs you more to pay today, state your answer with a negative sign (eg., -2000).

Answer 1

Given that,

for a 11 month vacation9 months from now, amount paid per month PMT = $4118 during vacation

interest rate = 4.85% compounded monthly

So, value of this annuity at month 9 is calculated using PV formula of annuity

PV = PMT*(1 - (1+r/n)^-N)/(r/n) = 4118*(1 - (1+0.0485/12)^(-11))/(0.0485/12) = $44218.49

So, present worth this amount today is

PV = 44218.49/(1 + 0.0485/12)^9 = $42642.07

But for this $33934 can be paid today.

If it is paid today, it will save 42642.07 - 33934 = $8708.07