To help their son buy a car on his 19th birthday, a boy's parents invest $1400 on his 10th birthday. If the investment pays an annual rate of 9% compounded continuously, how much is available on his 19th birthday?
A)$3118.94
B)$3147.07
C)$3040.65
D)$2534.00
E)$35,747.21

Question

Quizplus · Accepted Answer

We can use the formula for continuous compounding: A=Pe^(rt)
where A is the ending amount, P is the initial investment, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate in decimal form, and t is the time in years.

Since the investment is made for 9 years (from age 10 to age 19), we plug in P=1400, r=0.09, and t=9 into the formula:

A=1400*e^(0.09*9)
A=3147.07

Therefore, the available amount on his 19th birthday is $3147.07.

To Help Their Son Buy a Car on His 19th