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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.

Respuesta :

semsee45

Answer:

5 years and 5 months

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]

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:

[tex]\implies \sf 17474=7790\left(1+\dfrac{0.15}{12}\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{17474}{7790}=\left(1.0125}\right)^{12t}[/tex]

[tex]\implies \sf \ln\left(\dfrac{17474}{7790}\right)=\ln \left(1.0125}\right)^{12t}[/tex]

[tex]\implies \sf \ln\left(\dfrac{17474}{7790}\right)=12t \ln \left(1.0125}\right)[/tex]

[tex]\implies \sf t=\dfrac{\ln\left(\frac{17474}{7790}\right)}{12 \ln \left(1.0125}\right)}[/tex]

[tex]\implies \sf t=5.419413037...\:years[/tex]

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

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