Question

you want to establish a savings fund from which you will purchase some land to build a 2nd home in the mountains. you want to make this purchase in 20 years. You estimate the land will cost you 80,000. assuming you will earn 8% on account, how much per month do you need to free up from your budget to reach your goal?

Answer 1

Here, the deposits will be same every month, so it is an annuity. The future value of annuity is $80000. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity = $80000, P is the periodical amount, r is the rate of interest = 8%. Monthly rate = 8% / 12 = 0.6667% and n is the time period = 20 * 12 = 240

Now, putting these values in the above formula, we get,

$80000 = P * ((1 + 0.6667%)240 - 1 / 0.66667%)

$80000 = P * ((1 + 0.006667)240 - 1 / 0.006667)

$80000 = P * ((1.006667)240 - 1 / 0.006667)

$80000 = P * ((4.92680277081 - 1 / 0.006667)

$80000 = P * (3.92680277081 / 0.006667)

$80000 = P * 588.990966

P = $80000 / 588.990966

P = $135.83

So, the amount of money that we need to deposit each month is $135.83.