How much would $450 invested at the end of each quarter be worth in 10 years at 4% interest?

Question

After paying off a car loan or credit card, don't remove this amount from your budget. Instead, invest in your future by applying some of it to your retirement account

Answer 1

It depends on how often the interest is accrued. If it is accrued, say, quarterly, then you would have

 

(invested amount)*( (1 + (interest/100)/(number of quarters in one year)) ^((number of years)*(number of quarters in one year) - 1) + ... + 1)

= 450*(1.01^39 + 1.01^38 + 1.01^37 + ... + 1.01^1 + 1.01^0)

= 450*(1.01^40 - 1)/0.01

=45,000*0.4888637

=$21,998.87

 

Likewise, if the interest is accrued monthly, the amount would be

 

450*((1 + 4/1200)^119 + (1 + 4/1200)^118 + (1 + 4/1200)^117 + ... + (1 + 4/1200)^1 + 1)
= 450*( (1 + 4/1200)^120 - 1)/(1/300)
=$66,262.41

 

Answer 2

A = p(1 + r/n)^nt, where A = amount, p = principal, r = rate, n = number of calculations per year, t = time.

 

A = 450(1 + 0.04/4)^4·10

A = 450(1.01)⁴⁰

A = 450(1.4888)

A = 669.99

 

Your investment be worth $669.99.