1. -/3 pointsTGInterAlgHS 9.3.E05 EXAMPLE 5 To save for college, parents of a newborn child invest $12,000 in a mutual fund at 10% interest, compounded quarterly. (a) Find a function for the amount in the account after t years. (b) If the quarterly interest paid is continually reinvested, how much money will be in the account when the child is 18 years old? To write a function for the amount in the account after t years, we will substitute the given values for P,r, and k into the compound interest formula. Strategy The resulting equation will involve only two variables, A and t. Then we can write that equation using function notation. Why (a) When we substitute 12,000 for P, 0.10 for r, and 4 for k in the formula for compound interest, the resulting formula involves only two variables, A and t. Solution Since the interest is compounded quarterly, k-4. Express r: 10% as a decimal. 0.10)4t 12,000(1+ As Since the value of A depends on the value of t, we can express this relationship using function notation. 4t AC)- 12,01010) A(t) 12,0001 + A(t)-12,000(1 + 0.025% Evaluate: 01.0.025 A(t) 12,000(1.025)4 This exponential function has a base of 1.025 (b) To find how much money will be in the account when the child is 18 years old, we need to find A(18). A(18) 12,000(1.025)4(i8) substitute 18 for t. - 12,000(1.025)72 Use a scientific calculator and press these keys: 1200 x 1.025y 72 When the child is 18 years old, the account will contain How much money would be in the account after 18 years if the parents initially invested $20,500? (Round your answer to two decimal places.) Self Check