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The amount of money S(t) in an account with a 6% annual interest rate compounde…

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Wize University Calculus 1 Textbook > Applications of Differentiation for Business & Econ

Compound Interest

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The amount of money S(t) in an account with a 6% annual interest rate compounded continuously is given by:
S(t)=S0e0.06tS\left(t\right)=S_0e^{0.06t}
Where S0S_0 is the amount of money at time t=0 (the initial amount) and t is the time in years.

How long would it take for an investment to double?


More Compound Interest Questions:
Which investment option provides the best return?
Option X: an interest rate of 8.75% compounded annually
Option Y: an interest rate of 8.50% compounded daily
Q:\bf{Q:}You have $5,000 to invest and the investment option you're considering pays 6.5% compounded annually. How long will it take for your investment to double?
Q:\bf{}Q: Which investment option provides the best return?
Option X: an interest rate of 7.45% compounded annually
Option Y: an interest rate of 7.20% compounded daily
Aaron deposits $5,000 into his bank account that earns an annual effective interest rate of 3%. How much interest will Aaron earn over five years if he withdraws the interest as it's earned?
Q:\bf{Q:} You are offered the following two savings opportunities:
You can invest $750 today and receive $950 in 4 years.
You can invest $750 today in a GIC that guarantees 5.55% a year compounded annually.
Q:\bf{Q:} You have some money to invest and the investment option you're considering pays 3% compounded continuously. How long will it take for your investment to quadruple? (Round your answer to 2 decimal places)
Compound Interest
Find the annual interest rate such that a principle of 10,000 dollars will quadruple in 20 years given that it is continuously compounded.
Compound Interest
Given an initial investment of $7000 continuously compounded, what is the rate of annual interest required for this principle to double in 5 years?
Compound Interest
A very cautious individual stores his money both in the bank, and in a safe hidden underneath the floorboards below his bed. He keeps $5000 underneath his bed for a rainy day while investing the other $15000 into a savings account that grows 2% annually that is compounded continuously. Write an expression for the expected value of your total savings after 10 years.