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

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)\\\\(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)\\\\(400,000)/(e^(2.16))=P\\\\\large\boxed{46,130.05}`