Question

Suppose you invest $2000 at annual interest rate of 4.5 % How much money do you have in the account after five years?

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

To find the amount we use the formula:

$A=P\cdot \left(1+\frac{r}{n}\right)^{nt}$

Here:

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

Given

P=$2000

r=4.5%

n=4

t = 5 years

Calculating compounded quarterly

After plugging in the values

$A=2000\left(1+\frac{4.5\%\:}{4}\right)^{4\cdot \:5}$

$A=2000\left(1+\frac{0.045}{4}\right)^{4\cdot \:5}$

$A=2000\cdot \frac{4.045^{20}}{4^{20}}$

$A=\frac{125\cdot \:4.045^{20}}{2^{36}}$

$A = 2,501.50$

Thus, If you deposit $2000 into an account paying 4.5% annual interest compounded quarterly, you will have $2501.50 after five years.

Calculating compounded semi-annually

n = 2

$A=2000\left(1+\frac{4.5\%\:}{2}\right)^{2\cdot \:5}$

$A=2000\left(1+\frac{0.045}{2}\right)^{2\cdot \:5}$

$A=2000\cdot \frac{2.045^{10}}{2^{10}}$

$A = 2,498.41$

Thus, If you deposit $2000 into an account paying 4.5% annual interest compounded semi-annually, you will have $2,498.41  after five years.