Question

For his birthday, Tyrone's parents gave him $7,790.00 which they put into a savings account that earns 15% interest compounded monthly. When Tyrone

started college, he withdrew the entire balance of $17,474.00 and used it to pay for tuition. How long was the money in the
account? Round your answer to the nearest month.

Answer 1

5 years and 5 months

Explanation:

Compound Interest Formula

`\large \text{$ \sf A=P(1+(r)/(n))^(nt) $}`

where:

• A = final amount
• P = principal amount
• r = interest rate (in decimal form)
• n = number of times interest applied per time period
• t = number of time periods elapsed

Given:

• A = $17,474.00
• P = $7,790.00
• r = 15% = 0.15
• n = 12
• t = number of years

Substitute the given values into the formula and solve for t:

`\implies \sf 17474=7790\left(1+(0.15)/(12)\right)^(12t)`

`\implies \sf (17474)/(7790)=\left(1.0125}\right)^(12t)`

`\implies \sf \ln\left((17474)/(7790)\right)=\ln \left(1.0125}\right)^(12t)`

`\implies \sf \ln\left((17474)/(7790)\right)=12t \ln \left(1.0125}\right)`

`\implies \sf t=(\ln\left((17474)/(7790)\right))/(12 \ln \left(1.0125)\right)}`

`\implies \sf t=5.419413037...\:years`

Therefore, the money was in the account for 5 years and 5 months (to the nearest month).