Question

Suppose that ​55 comma 00055,000 is invested at 3 and one half3 1 2​% ​interest, compounded quarterly. ​a) Find the function for the amount to which the investment grows after t years. ​b) Find the amount of money in the account at tequals=00​, 44​, 77​, and 10 years.

Answer 1

(a)
`A(t) = 55000(1.0035)^(4t)`

(b) At t = 0, A = 55,000

At t = 4, A = 58,162.19

At t = 7, A = 60,652.57

At t = 10, A = 63,249.60

Explanation:

(a) The amount on a compound interest is given by

`A(t) = P\left(1+(R)/(100)\right)^T`

P is the principal invested, R is the rate and T is the time.

The principal is 55,000. With the interest compounded quarterly, there are four compundings in a year. Hence each year will have four periods.

The function for the amount is then

`A(t) = 55000\left(1+(3.5)/(100)\right)^(4t) = 55000(1.0035)^(4t)`

(b)

At t = 0,

`A(0) = 55000(1.0035)^(4*0) = 55000`

At t = 4,

`A(4) = 55000(1.0035)^(4*4) = 58162.19`

At t = 7,

`A(7) = 55000(1.0035)^(4*7) = 60652.57`

At t = 10,

`A(0) = 55000(1.0035)^(4*10) = 63249.60`