Your grandparents give you $1000 for your tenth birthday to invest for your college education. You research some investment companies around town and find one that pays you 4.2% and compounds quarterly. If you leave the money in your account until your 18th birthday, how much money will you have? Show all your work.

Respuesta :

Answer:

$ 13,968.90

Step-by-step explanation:

  • You are given the money at 10 years old
  • Invest it until you're 18, so that's 8 years
  • This is compound interest, so use the formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
  • A is the total amount with interest
  • P is the principal or starting amount 10000 dollars
  • r is the rate (percentage): 4.2%, use the decimal form in the equation
  • n is the number of times you are compounding; in this case, it is compounded quarterly. Quarterly means every quarter of a year or 3 months, so it is compounded 4 times a year, n is 4
  • t is the time, so that's 8 years
  • [tex]A=10000(1+\frac{0.042}{4})^{4\times8}= 13,968.90[/tex]
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