Question

2.) What amount presently must be invested earning 5.25% compounded continuously

so that it will grow up to be worth $25,000 12 years from now?

Answer 1

An initial investment (P) compounded continuously with a rate of interest (r) in time (t) will grow to amount (Q) is given by:

Q = P * e^(rt)

Q=25000, r=0.0525, t=12

25000 = P * e^(0.0525*12)

1.8776P = 25000

P = 13314.8

Answer 2

The amount A resulting from a principal amount P being invested at rate r compounded continuously for time t is given by

... A = P·e^(rt)

FIll in your given values and solve for P.

... 25000 = P·e^(0.0525·12) = P·e^0.63

... P = 25000/e^0.63 ≈ 13314.80 . . . . . divide by the coefficient of P

The amount that must be invested is $13,314.80.