Question

A total of $10,000 is invested at an annual interest rate of 3%. Find the balance after 5

years if the interest is compounded a) quarterly and b) continuously.

Answer 1

Explanation:

We will need 2 different equations for this problem. For compounding a certain number of times a year, the formula is

`A(t)=P(1+(r)/(n))^(nt)` so let's do that first. Filling in we get

`A(t)=10000(1+(.03)/(4))^{(4)(5)` and simplifying a bit gives us

`A(t)=10000(1+.0075)^(20)` and a bit more,

`A(t)=10000(1.0075)^(20)` and then

A(t) = 10000(1.161184142) so

A(t) = 11611.84

Then for the compounding continuously, the formula is

`A(t)=Pe^{rt`

`A(t)=10000e^((.03)(5))` and simplify a bit to\

`A(t)=10000e^(.15)` Now raise e to the power of .15 on your calculator to get

A(t) = 10000(1.161834243) so

A(t) = 11618.34

Not too much of a difference between the 2 values at the end.