Question

Jamie deposits 400 into a savings account. The account has an interest rate of 5%, compounded quarterly. Right to function that gives you The amount of money in dollars, J(t) in t years after the initial deposit

Answer 1

Given:

Initial value = 400

Interest rate = 5% compounded quarterly.

To find:

The function that gives you the amount of money in dollars, J(t) in t years after the initial deposit.

Solution:

The formula for amount is:

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

Where, P is principal, r is the rate of interest in decimals, n is the number of times interest compounded in an year and t is the number of years.

The interest rate is 5% compounded quarterly. So, r=0.05 and n=4.

Substituting $P=400,\ r=0.05,\ n=4$ in the above formula, we get

$A=400\left(1+\dfrac{0.05}{4}\right)^{4t}$

$A=400\left(1+0.0125\right)^{4t}$

$A=400\left(1.0125\right)^{4t}$

The required function notation is:

$J(t)=400\left(1.0125\right)^{4t}$

Therefore, the amount of money in dollars, J(t) in t years after the initial deposit is $J(t)=400\left(1.0125\right)^{4t}$.