# PV question

Yikes! I have progressed so far and have forgotten basic quant. John Doe needs 50k as a down payment for a purchase in 3 years Currently has 10k and can earn 10% a year. How much necessary to save each year to meet goal? What is the correct formula/

PV = 10,000 FV = 50,000 PMT = ? I = 10% N = 3 for annual compounding.

just try to solve it algebraically. 50 = 10*1.1^3 + X*1.1^2 + X; solve for X i got about \$16,600 doing it on scratch paper

the formula is a future value of an annuity - you can’t solve it using formula Mlh97 provided (well you can but the answer won’t answer what the question is asking) because it doesn’t break out the annual savings componenet (for instance, in year one, you save 0 according to his formula and then a crapload in year two and three…which isn’t what hte question is asking you for). for an annuity with pmt at the end of year its approx. \$11k, for an annuity due, its about \$10k.

you’re right; my formula is wrong. it should be 50 = 10*1.1^3 + X*1.1^2 + X*1.1 + X and this assumes you start with 50k now and don’t make your first payment until the end of the first year. all i’m saying is that this is the kind of question where you shouldn’t need a simple formula; just figure it out. i client recently called up and asked if we had a present value of \$1 table. i just built one in excel and emailed it back to him. you don’t need to be a quant to know how the math works on pv.

mlh - you’re usinga simple FV formula, not a FV of an annuity formula…the formula for a FV annuity is: FVoa = PMT [((1 + i)^n - 1) / i]

look, the X is there three times. this means that the X payment is made three times, or a three year annuity. a fv of annuity is only a series of each individual annuity payment, each with its own simple fv calc. tell me why solving for X in this formula is wrong. i just solved for X my way and got \$11,085.

Joe could also save nothing for the first 2.5 years and then start working overtime and save up the remaining 40K in the last six months. This assumes he will *not* put the initial 10K in the bank, of course. This solution has the distinct advantage that you do not need to know anything about compounding.

^ | Pardon? read the question. it says how much he must save PER YEAR in order to achieve his goal…

I’m with FourCastles. Nowhere does the question state that an equal amount must be saved each year…

you’re right - nowhere does it say an equal amount must be saved each year but this is a classic intro finance annuity question that whoever is marking it would assume equal payments. you could submit any permutation of payments, but i know my former profs wouldn’t give me full marks for doing so.