Problema Solution
Recall that if P dollars is invested in an account at an interest rate r compounded continuously then the amount A( called the future value of P) in the account t years from now on will be A=Pe^rt. Solving the equation for P, we get P=Ae^-rt. In this formulation, P is called the present value of the investment.
(a) Find the present value of $100,000 at 5% compounded continuously for 15 years.
(b) Find the interest rate compounded continuously that is needed to have $25,00 be the present value of $125,000 in twenty years
Answer provided by our tutors
(a) Find the present value of $100,000 at 5% compounded continuously for 15 years.
A = $100,000
r = 0.05 or 5%
t = 15 years
P = the present value
P=Ae^-rt
P = 100000*e^(-0.05*15)
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P = $47,236.66
The present value is $47,236.66.
(b) Find the interest rate compounded continuously that is needed to have $25,00 be the present value of $125,000 in twenty years
P = $25,000
A = $125,000
t = 20 years
r = the interest rate as a decimal
A=Pe^rt
125000 = 25000*e^(20r)
25000*e^(20r) = 125000
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r = 0.0805 or 8.05%
The interest rate is 8.05%.