SOLUTION: How much money should you deposit into a certificate of deposit that pays 4 % a year compounded continuously to have $70,000 in the account in 18 years?
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Question 1071618: How much money should you deposit into a certificate of deposit that pays 4 % a year compounded continuously to have $70,000 in the account in 18 years? Answer by math_helper(2461) (Show Source):
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A good formula to know for discrete compounding (i.e. annually, quarterly, monthly, daily):
where
F=future value
P=present value
r=annual interest rate (expressed as a decimal)
n=number of compounding periods per year
t=number of years
—
But for continuous compounding, we need to let , and that formula becomes:
[ This comes from Lim n—>, by making the substitution in the discrete compounding formula above of m=n/r you get n=rm and you can see the 'e' part of the limit, raised to the rt power. ]
In this problem, F=70000 and we want to know P:
dollars
