how much will your savings be worth after 10 years?

Question

How much should you invest each month in order to have $600,000 if your rate of return is 4.8% compounded monthly and you want to achieve your goal in 40 years?

How much interest will you earn?

How much should you invest each month in order to have $600,000 if you want to achieve your goal in 20 years?

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

Answer 1

Hello Jessica,

 

We'll be returning to this general equation several times here:

 

     S = ar(1 - rⁿ)/(1 - r)       (Eq. 1)

 

S is the account balance after n months of depositing a dollars each month. r is equal to 1 + the monthly interest rate (for this problem, r = 1.004, since an annual interest rate of 4.8% equates to 0.4% interest compounded each month).

 

For the first part of your problem, S = $600,000 and n = 480 months (12 months x 40 years). Use Eq. 1 to find a.

 

The total interest you'd earn would be equal to S - P, where P = an. It's an impressive number!

 

For the second part of your problem, S = $600,000 and n = 240 months (12 months x 20 years). You'll need to find a.

 

For the third part of your problem, use the value for a you received in the second part, and use n = 120 months (12 months x 10 years). Find S.

 

Now, if only more people (myself included) would go visit their banks and actually do this...  :)

Answer 2

We are dealing with the future value of an ordinary annuity. You can lookup the formula and solve for the payment, or you can use a spreadsheet function or financial calculator. The simplest approach is a financial calculator, but you have to understand compound interest and annuities. The variables are

 

PV = 0

FV = 600,000

N = 40 years = 480 months

i% = 4.8% = .4%

PMT = ?

 

PMT = $412.51

 

As to how much interest you earned, you paid $412.51 x 480 = $198,005 so $600,000 - $198,005 = $401,995

For 20 years, PMT - $1,437.79 per month

 

PV = 0
FV = ?
N = 10 years = 120 months
i% = 4.8% = .4%
PMT = 1,437.79

FV = $229,486.94

 

The important point is to define the four known variables and solve for the unknown. You have to interpret the problem carefully.