Question

Suppose you want to have $400,000 for retirement in 30 years. Your account earns 5% interest.

a) How much would you need to deposit in the account each month?

b) How much interest will you earn?

You deposit $2000 each year into an account earning 6% interest compounded annually. How much will you have in the account in 35 years?

A man wants to set up a 529 college savings account for his granddaughter.

How much would he need to deposit each year into the account in order to have $70,000 saved up for when she goes to college in 18 years, assuming the account earns a 8% return.

Annual deposit: $

Answer 1

First question is being answered here:

1 (a) Here, the deposits will be same every year, so it is an annuity. The future value of annuity is $400000. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity = $400000, P is the periodical amount, r is the rate of interest = 5%. Monthly rate = 5% / 12 = 0.4167% and n is the time period = 30 * 12 = 360 months

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

$400000 = P * ((1 + 0.4167%)360 - 1 / 0.4167%)

$400000 = P * ((1 + 0.004167)360 - 1 / 0.004167)

$400000 = P * ((1.004167)360 - 1 / 0.004167)

$400000 = P * ((4.46827825053 - 1 / 0.004167)

$400000 = P * (3.46827825053 / 0.004167)

$400000 = P * 832.320194513

P = $400000 / 832.320194513

P = $480.58

So, the amount of money that we need to deposit each month is $480.58

(b) Total money deposited = $480.58 * 360 = $180617.1

Future value or accumulated amount = $400000

Interest earned = $400000 - $173008.8 = $226991.2