Question

The amount of money, in dollars, in an account after t years is given by A = 1000(1.03)t. The initial deposit into the account was $a0 and the interest rate is a1% per year. Only enter numbers in the boxes. Do not include any commas or decimal points.

Answer 1

The initial deposit into the account was $1000 and the interest rate is 3% per year

Answer 2

Initial value, a0 = $1000

Rate of interest, a1 = 0.03 = 3%

Explanation:

The amount of money in an account after t years is given by the expression :

`Amount = P(1+(Rate)/(n))^(n* Time)...........(1)`

where P is the initial amount or the Principal value of the account, n is the number of times the interest is compounded in a year.

Now, According to question, the amount of money in an account after t years is given by the expression :

`Amount = 1000(1.03)^t\\\\\text{This expression can be rewritten as : }\\\\Amount = 1000(1+(0.03)/(1))^(1* t)`

Now, on comparing the above expression with (1),

We get, P = 1000 , Time = t years , n = 1 and Rate = 0.03

Hence, Initial value, a0 = $1000

Rate of interest, a1 = 0.03 = 3%