Question

Derrick will need $39,500 in 10 years for college tuition. How much should his parents invest now at 9.5% annual interest, compounded daily, to reach this goal?

$3,950

$2,257.69

$10.82

$15,278.16

Answer 1

His parents should invest $15,278.16 to reach this goal ⇒ 4th answer

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:

`A=P(1+(r)/(n))^(nt)` , 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

∴
`39500=P(1+(0.095)/(365))^(365*10)`

∴
`39500=p(2.58539)`

- Divide both sides by 2.58539

∴ P = $15278.16

∴ His parents should invest $15,278.16 to reach this goal