I need help with this Algebra question for my final

Question

Suppose $15,000 is invested in a retirement account that earns 5% interest, compounded monthly. How much is in the retirement after 10 years. How much more money would be in the account if it was compounded continuously for 10 years at 5% interest?

Answer 1

The first step I use to calculate these problems are to recognize the formulas, then assign the variables. For monthly compounded interest, we use P(1+r/n)^nt, and for continuous formulas we use Pe^rt . Now we need to assign the variables.

P is the amount invested, being 15,000, r is the rate of interest, which is 5%, or .05, n is the amount of compounding, or in this case monthly, meaning 12/year, which is simply 12, and t is the total amount of years being 10. Since e is a constant, 2.718... we simply memorize this value, or use a calculator if allowed.

For the first part, we get our total = 15,000(1+.05/12)¹²⁽¹⁰⁾ = 24,705.14

For the second part, we get our total = 15,000e^.05(10) = 24,730.82

We can subtract the compounded answer from the continuous answer to get the difference.

24,730.82 - 24,705.14 = 25.68

Answer 2

A=15000(1+.05/12)^12(10) for 10 years of monthly compounding

=15000(1.0046111...)^120 =$

A=15000e^.05(10)= 15000e^5 = $24,730.82

Formulas are A=P(1+r/n)^nt where r= annual interest, n=number of compounding per year, t=years

and that collapsed to A=Pe^rt when n approaches infinity, for continuous compounding