Question

2. You want a savings account to grow from $1,000 to $5,000 within two years. Assume the bank provides a 3.2% annual interest rate compounded monthly. What is the math formula to calculate how much you must deposit each month to meet your savings goal?

Answer 1

First, find the value that becomes after two years compounding montly of $1000 at 3.2%

Future value=$1000*(1+(3.2%/12))^(2*12)=$1066.0

So, you have to accrue the remaining $3934 in two years.

The math formula for each month payments=(( FV*i)/(1+i)^(n))-1

i=3.2%/12=0.00267

n=2*12=24

Monthly deposit=(3934*0.00267)/((1+0.00267)^24)-1

Montly depost=$158.95

This we can cross check with PMT function in EXCEL

=PMT(rate,nper,pv,fv,type)

=PMT(0.267%,24,0,3934,0)

PMT=$158.95