Question

You are planning to make monthly deposits of $490 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years?

b)  In the previous problem, suppose you make $3,600 annual deposits into the same

Answer 1

formula = Maturity Amount = Installment * [ (1 + r)^n - 1] / r

Putting the values from the problem,

a) Monthly deposit,

A = $490 * [ (1 + 0.10/12)^30*12 - 1 ] / 0.10/12

= $490 * 19.8350387 - 1 / (0.10 / 12)

= $1,107,500.30

b) Annual deposit,

A = $3600 * ( 1 + 0.10)^30 - 1 / 0.10

= $3600 * 17.4494 - 1 / 0.10

= $592,178.40

Answer 2

SOLUTION :

a.

Monthly compounding.

Monthly deposit, A = 490 ($) (starting from the next month)

Monthly interest rate, r = 10/12 % = 10/1200 = 1/120 in fractions.

=> 1 + r = 121/120 

Periods, n = 30 * 12 = 360 months

So, 

FV after 30 years (360 months)

= A((1 + r)^n - 1) / r

= 490 * ((121/120)^360 - 1) / (1/120)

= 1107639.08 ($)  (ANSWER).

b.

If annual deposit means annual compounding.

Annual deposit, A = 3600 ($) (starting from the next year assumed )

Annual interest rate, r = 10 % = 0.10 in decimals

=> 1 + r = 1.10 

Periods, n = 30 years

So, 

FV after 30 years 

= A((1 + r)^n - 1) / r

= 3600(1.10^30 - 1)/0.10

= 592178.48 ($)  (ANSWER).