Algebra Finance

Question

You decide to contribute to a mutual fund that averages 4.1% return per year. If you contribute $275 quarterly.

a) How much will be in the account after 10 years?

b) How much of this money did you deposit?



c) How much of this money is interest earned? 

Answer 1

Given:

rate of return = (interest rate) = 4.1% or 4.1/100 = 0.041

contribution amount = (principal) = $275

deposit frequency = quarterly, which means 4 times per year (4t)

a) How much will be in the account after 10 years? So, t = 10 years

Using the formula for the future value of an annuity (contribution of same amount), but accounting for the quarterly deposit frequency:

FV = Contribution * [ (1+r/4)^4t - 1] / (r/4)

FV = 275 * [ (1+0.041/4)^4(10) - 1] / (0.041/4)

FV = 275 * [ 0.503676334 ] / (0.01025)

FV = 275 * 49.13915454

FV = 13,513.27

There will be $13,513.27 in the account after 10 years.

$13,513.27 is composed of the principal amount plus accumulated interest.

Interest = Principal (beginning balance) * Interest rate * # of periods

= 275 * 0.041/4 * 4(10)

= 112.75

Principal = 13,513.27 - 112.75 = 13,400.52

b) How much of this money did you deposit? $13,400.52

c) How much of this money is interest earned? $112.75