From Susan

secondary level question;
Future value of money
Occupation: Nurse

If one were to invest $115 a month for 20 years and expect a 4% annual return, what is the value of this money in 20 years?

Thank you

Hi Susan,

For an ordinary annuity (the type of investment you are contemplating), the future value, S, of n equal payments of R dollars, each made at the end of n consecutive interest periods with an interest rate of i per period, is given by the formula:

S = [R(1+i)n - 1]/i

For your annuity:

R = 115
n = 240

The only tricky part is to find i, the interest rate per month. Since you don't specify in your request, I will assume that interest is being compounded monthly. Simply dividing 4% by 12 gives you a good approximation of the monthly interest rate, but not exact. To get the exact rate you must consider that (1 + i)12&nbap;=&nbap;1.04. Thus i will be equal to the twelfth root of 1.04, minus 1.

To show you how small the difference in the interest rates is, using  0.04/12 you get 0.00333333 Using the second method, you get 0.00327374

Now that we have all the values we need (I will use the second value we found for i since it is more precise) to use the formula, we can plug the numbers in to see that at the end of 20 years, you will have a total of $41,841.80.

If we had used the first value for i, the amount would have been $42,179.08, slightly higher.

A quick search reveals that the internet has numerous websites with financial calculators that can assist you in these types of calculations. All you have to provide them with is the values for the payments, interest rate and length of investing.

Hope this helps,

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