Question

How much should you deposit at the end of each month into an investment account that pays

8.5 % compounded monthly to have

$ 1 million when you retire in

43years?

How much of the $1

million comes from​ interest?

Answer 1

Here, the deposits will be same every month, so it is an annuity. For calculating the monthly deposits, we will use the following future value of annuity formula:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity = $1000000, P is the periodical amount, r is the rate of interest = 8.5% compounded monthly, so monthly rate = 8.5% / 12 = 0.708333% and n is the time period = 43 * 12 = 516 months

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

$1000000 = P * ((1 + 0.708333%)516 - 1 / 0.7083333%)

$1000000 = P * ((1 + 0.007083333)516 - 1 / 0.00708333)

$1000000 = P * ((1.00708333)516 - 1 / 0.00708333)

$1000000 = P * ((38.1725183891 - 1 / 0.007083333)

$1000000 = P * (37.1725183891 / 0.007083333)

$1000000 = P * 5247.88497374

P = $1000000 / 5247.88497374

P = $190.55

So, the amount of money that we need to deposit each month is $190.55

Total amount deposited = $190.55 * 516 = $98325.33

Interest = Future value - Total amount deposited

Interest = $1000000 - $98325.33 = $901674.67