Question

Currently, I have $2,500 in my bank account that pays 6% APR with monthly compounding. In order to have $12,000 in this account in 5 years, how much money should I add to this account each month starting from next month?

Answer 1

Given,

Current balance = $2500

APR = 6% or 0.06

Future value = $12000

Number of years (n) = 5 years

Solution :-

Monthly rate (r) = 0.06/12 = 0.005

Number of months (n) = 5 years x 12 = 60

Let Monthly deposits be 'M'

Now,

Future value = [M/r x {(1 + r)ⁿ - 1}] + [Current balance x (1 + r)ⁿ]

$12000 = [M/0.005 x {(1 + 0.005)⁶⁰ - 1}] + [$2500 x (1 + 0.005)⁶⁰]

$12000 = [M/0.005 x {(1.005)⁶⁰ - 1}] + [$2500 x (1.005)⁶⁰]

$12000 = [M/0.005 x {1.3488501525 - 1}] + [$2500 x 1.3488501525]

$12000 = [M/0.005 x 0.3488501525] + [$3372.12538125]

$12000 - $3372.12538125 = M/0.005 x 0.3488501525

$8627.8746188 = M/0.005 x 0.3488501525

$8627.8746188 x 0.005/0.3488501525 = M

$123.66 = M

You should add $123.66 each month.