Compound interest

Question

A particular savings account has a 7% interest rate.

1) If you invest $1200 into the account and it compounds monthly, what will the balance be after 5 years?

2) How much money would you need to invest into the account if it compounds quarterly and you’d like the balance to

be $10,000 after 5 years?

3) If the account compounds continuously, how long will it take for the principal to double?

Answer 1

1) FV = PV(1+i)^t is correct for an i as an annual rate and t is years. (1200)(1+.07)⁵

2) Compounding for a smaller interval that goes n times into a year

FV = PV(1+i/n)^nt where n is 4 for quarters and 12 for monthly. In this case you know the future values you want, and are solving for PV.

3) Compounding continuously has the equation FV =PVe^it where i is your yearly rate of interest. This is the result of the formula in (2) taken to the limit as n__> infinity. In this case, you solve:

FV/PV = 2 = e^.07t for t by taking the ln of both sides.

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