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Future Value of Single Cash Flow for Multiple-Period Investment with Continuous Compound Interest

Future Value of Single Cash Flow for Multiple-Period Investment with  Continuous Compound Interest
Future Value with a Single Cash Flow:

Time value of money for a single cash flow is a cash inflow or outflow that investors or lenders received from or paid to once respectively for specific periods.

Future value (FV) refers to the amount of money an investment or present value (PV) will grow for specific periods of time at specific interest rate.

Future Value = Present Value + all earned interests

Multiple-Period Investment:

Multiple-period investment may be investment for more than one year. Term multiple-period can refer to more than one day or one month investment, so it isn’t always more than one year investment.

If period investments are based on one day, one month or one year etc., so discount rates are based on one day, one month or one year respectively.

Definition of Continuous Compound Interest:

 We could compound semiannually, quarterly, monthly, daily, hourly, each minute, or even more often by using FV=PV(1+r/f)ft, but when it is compounded discount rate continuously, so we cannot use this formula.

Formula of Future Value with Continuous Compound Interest for Multiple-Period Investment:

FV=PV*ert

which

e : is a constant , and e≈2.7182

PV: Present Value or principal is worth today

FV: Future value is worth in the future

r : Interest rate, rate of return, or discount rate per period , but not always one year.

t : time is referred to number of periods of investment

 Question

Miss. Theary Chana invested $2,000 with financial institution at a continuously compounded rate of 10 percent for two year.

What is the value of her wealth at the end of two year?

Solution

FV=PV*ert=2,000*e0.1*2=2,000*1.2214=$2,443

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