On a day of a child's birth, a deposit of $5,000 is made in a trust fund that pays 7.5% interest compounded monthly.

Question

A.Write a model.

 

B.How much will the child receive on their 18th birthday?

Answer 1

A = P ( 1 +  (r/n) ) ^nt

 

 

P = 5000, r = 0.075 and n= 12 since the interest is compounded monthly

 

 

A  = 5000 ( 1 + (0.075/12))^ 12t

 

 

In order to find the amount that the child will receive by her 18th birthday plug in 18 as the value for t in the above equation

 

A = 5000 ( 1 + (0.075 / 12 ) )^ 12(18)

 

A = $ 19206 

 

The  child would have an amount of $19,206 in her trust by the time she turns 18.

Answer 2

Compound interest formula:  A = P(1+r/n)^nt

A = future amount

P = principal investment = $5,000

r = interest rate as a decimal = .075

n = number of times per year interest is compounded = 12

t = time in years

 

Model:  A = 5000(1 + .075/12)^12t

 

B.  On 18th birthday t = 18

 

     A = 5000(1+.075/12)¹²⁽¹⁸⁾

        = 5000(1.00625)²¹⁶

        = $19,206.27

 

Hope this helps.  Let me know if there are any questions.  Good luck.