Question

Suppose an individual wants to have exactly $400,000 available for her child's education. (a) Find the amount that would have to be invested at 12% compounded continuously, if the number of years until college is 9 years. (Round your answer to the nearest cent.) (b) Find theamount that would have to be invested at 12% compounded continuously, if the number of years until college is 18 years. (Round your answer to the nearest cent.)

Answer 1

Answer:  a) $135,838.21           b) $46,130.05

Step-by-step explanation:

$A=P\cdot e^{rt}$

• A: accrued amount (balance)
• P: principal (initial amount invested)
• r: interest rate (in decimal form)
• t: time

(a) Given:

• A = 400,000
• P = unknown
• r = 12% = 0.12
• t = 9

$400,000=P\cdot e^{(0.12)(9)}\\\\400,000=P\cdot e^{1.08}\\\\\dfrac{400,000}{e^{1.08}}=P\\\\\large\boxed{135,838.21}$

(b) Given:

• A = 400,000
• P = unknown
• r = 12% = 0.12
• t = 18

$400,000=P\cdot e^{(0.12)(18)}\\\\400,000=P\cdot e^{2.16}\\\\\dfrac{400,000}{e^{2.16}}=P\\\\\large\boxed{46,130.05}$