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

87.14 years

Explanation:

for plato

Answer 2

Answer: 28.43 years

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\\\\(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`