Answer:
His parents should invest $15,278.16 to reach this goal ⇒ 4th answer
Step-by-step explanation:
* Lets explain how to solve the problem
- Derrick will need $39,500 in 10 years for college tuition
∴ The future amount is $39,500
∴ The time for investment is 10 years
- P is the money his parents invest now at 9.5% annual interest,
compounded daily
∴ The rate is 9.5% per year compounded daily
- The formula of the compounded interest is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
# A is the future value of money
# P is the value of investment
# r is the rate of interest in decimal
# t is the time of investment
# n is the period of the time
∵ A = $39,500
∵ t = 10
∵ r = 9.5/100 = 0.095
∵ n = 365 ⇒ compounded daily
- Lets use the formula above to find P
∴ [tex]39500=P(1+\frac{0.095}{365})^{365*10}[/tex]
∴ [tex]39500=p(2.58539)[/tex]
- Divide both sides by 2.58539
∴ P = $15278.16
∴ His parents should invest $15,278.16 to reach this goal
