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+(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+(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)`.