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

Answer:

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

(3)t=16.93 years

Step-by-step 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.

$1000000= 318000(1.07)^t\\(1.07)^t=\frac{1000000}{318000} \\(1.07)^t=3.1447\\Log_{1.07}\frac{1000000}{318000}=t\\t=16.93$

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