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

Answer:

8 months

Step-by-step explanation:

$17,474.00 - $7,790.00 = $9,684

15% of $7,790 : $7,790 x 0.15 = $1,168.50

$9,684 / $1,168.50 = 8.2876

8.2876 = about 8

Im kinda tired, lmk if you want a more in depth explanation or have a question, just really want to answer

Answer 2

Answer:

5 years and 5 months

Step-by-step explanation:

Compound Interest Formula

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

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:

$\implies \sf 17474=7790\left(1+\dfrac{0.15}{12}\right)^{12t}$

$\implies \sf \dfrac{17474}{7790}=\left(1.0125}\right)^{12t}$

$\implies \sf \ln\left(\dfrac{17474}{7790}\right)=\ln \left(1.0125}\right)^{12t}$

$\implies \sf \ln\left(\dfrac{17474}{7790}\right)=12t \ln \left(1.0125}\right)$

$\implies \sf t=\dfrac{\ln\left(\frac{17474}{7790}\right)}{12 \ln \left(1.0125}\right)}$

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

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