Question

Tony is evaluating his retirement savings. He currently has $318,000 in his account which earns an interest rate of 7% compounded annually. He wants to determine how much he will have in the account in the future, even if he makes no additional contributions to the account.

1) Write a function, A(t), to represent the amount of money that will be in his account in t years.

2) Graph A(t) where 0≤t≤20 on a set of axes

3) Tony's goal is to save $1,000,000. Determine algebraically, to the nearest year, how many years it will take for him to achieve his goal.

4) Explain how your graph of A(t) confirms your answer.

Answer 1

(1)
`A(t)= 318000(1.07)^t`

(3)t=16.93 years

Explanation:

For a Principal Saved at Compound Interest, the Amount accrued is derived by the function:

`A(t)= P(1+r)^t`

When:

(1)P=$318,000

r=7%=0.07

`A(t)= 318000(1+0.07)^t\\A(t)= 318000(1.07)^t`

(2)See Attachment

(3)If Tony's goal is to save $1,000,000.

`1000000= 318000(1.07)^t\\(1.07)^t=(1000000)/(318000) \\(1.07)^t=3.1447\\Log_(1.07)(1000000)/(318000)=t\\t=16.93`

(4)The graph confirms the result as the $1000000 Mark on the y-axes occurs almost at x=17