Question

tina wants to save money for school. tina invests $400 in an account that pays an interest rate of 4%. how many years will it take for the account to reach $12,200? round your answer to the nearest hundredth

Answer 1

Answer:   28.43 years

Step-by-step explanation:

$A = P(1 + r)^t\quad \text{where}$

• A is the amount accrued
• P is the principal (initial) amount invested
• r is the interest rate (in decimal form)
• t is the time (in years)

$12,200=400(1+0.04)^t\\\\3.05=(1.04)^t\qquad \rightarrow divided\ both\ sides\ by\ 400}\\\\ln(3.05)=ln(1.04)^t\rightarrow applied\ natural\ log\ (ln)\ to\ both\ sides\\\\ln(3.05)=t\ ln(1.04)\rightarrow applied\ log\ rule\ to\ eliminate\ exponent\\\\\dfrac{ln(3.05)}{ln(1.04)}=t\qquad \rightarrow divided\ ln(1.04)\ from\ both\ sides\\\\\\28.43=t\qquad \rightarrow used\ calculator\ to\ simplify$

Answer 2

Answer:

87.14 years

Step-by-step explanation:

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