Question

Suppose you invest $200 a month for 7 years into an account earning 9% compounded monthly. After 7 years, you leave the money, without making additional deposits, in the account for another 22 years. How much will you have in the end?

Answer 1

Answer:

$172,806.37.

Step-by-step explanation:

Total = [ P(1+r/n)^(nt) ] + [ PMT × (((1 + r/n)^(nt) - 1) / (r/n)) ] * (1 + r/n)

is the formula  for the amount left after the first 7 years where the money is deposited at the beginning of each month and P = initial amount,  PMT = monthly payment, r = rate as a decimal and t = time in years.

Total after the first 7 years

=  [ 200(1+0.09/12)^(7*12) ] + [ 200 × (((1 + 009/12)^(7*12) - 1) / (0/09/12) ] * (1 + 0.09/12)

= 374.64 +  (200 * 0.8732019633) / (0.09/12) * (1 + 0.09/12)

= 374.64 + 23485.386 * 1.0075

= $24.036.17

Total after a further 22 years:-

=  24.036.17(1 + 0.09/12)^(12*22)

=  $172,806.37 (answer).