Question

Miranda wants to give her 14-year-old daughter $20,000 when she turns 18. How much does she need to put in the bank now if the interest rate is 10 percent

per year?
future value=Px(1+0)
present value = a to
A $12,418.43
B. $13,660.27
C. $15,026.30

Answer 1

The future principal amount invested is $13,660.27 .

Explanation:

Given as :

The Amount that saved for future = A = $20,000

The bank applied rate of interest = r = 10%

The time period of loan = t years

Now As Miranda's daughter is 14 year now, and she will give money when her daughter turns 18

∴ The time period of loan = t = 4 years

Let the future principal amount invested = $p

Now, From Compound Interest method

Amount = principal ×
`(1+(\textrm rate)/(100))^(time)`

Or, A = p ×
`(1+(\textrm r)/(100))^(t)`

Or, $20,000 = p ×
`(1+(\textrm 10)/( 100))^(4)`

Or, $20,000 = p ×
`(1.1)^(4)`

Or, $20,000 = p × 1.4641

∴ p =
`(20,000)/(1.4641)`

i.e p = $13,660.269

So, The future principal amount invested = p = $13,660.27

Hence, The future principal amount invested is $13,660.27 . Answer