Question

I deposit $1000 a month in an account paying 4.23% for 15 years. You deposit $350 a month in an account with the same yield for 30 years. How much will be in each account? How much total interest will each account produce?

Answer 1

Here, since the deposits will be same every month, so it is an annuity. We need to calculate future value of annuity. 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, P is the periodical amount, r is the rate of interest = 4.23%. Monthly rate = 4.23% / 12 = 0.3525% and n is the time period

Calculation of Future value of $1000 a month for 15 years:

where, FVA is future value of annuity, P is the periodical amount = $1000, r is the rate of interest = 0.3525%  and n is the time period = 15 * 12 = 180

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

FVA = $1000 * ((1 + 0.3525%)180 - 1 / 0.3525%)

FVA = $1000 * ((1 + 0.003525)180 - 1 / 0.003525)

FVA = $1000 * ((1.003525)180 - 1 / 0.003525)

FVA = $1000 * ((1.88397576944 - 1 / 0.003525)

FVA = $1000 * (0.88397576944 / 0.003525)

FVA = $1000 * 250.773267927

FVA = $250773.27

So, after 15 years, there will be $250773.27 in the account.

Calculation of Total interest:

Total payments = $1000 * 180 = $180000

Future value = $250773.27

Total interest = Future value - Total payments

Total interest = $250773.27 - $180000 = $70773.27

Calculation of Future value of $350 a month for 30 years:

where, FVA is future value of annuity, P is the periodical amount = $350, r is the rate of interest = 0.3525%  and n is the time period = 30 * 12 = 360

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

FVA = $350 * ((1 + 0.3525%)360- 1 / 0.3525%)

FVA = $350 * ((1 + 0.003525)360 - 1 / 0.003525)

FVA = $350 * ((1.003525)360 - 1 / 0.003525)

FVA = $350 * ((3.54936469985 - 1 / 0.003525)

FVA = $350 * (2.54936469985 / 0.003525)

FVA = $350 * 723.224028325

FVA = $253128.4

So, after 30 years, there will be $253128.4 in the account.

Calculation of Total interest:

Total payments = $350 * 360 = $126000

Future value = $253128.4

Total interest = Future value - Total payments

Total interest = $253128.4 - $126000 = $127128.4