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# Time Value Analysis

1. If you deposit money today into an account that pays 6.5 percent interest, how long will it take for you to double your money?

2. John Roberts has \$42,180.53 in a brokerage account, and he plans to contribute an additional \$5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12 percent. If John's goal is to accumulate \$250,000 in the account, how many years will it take for John to reach his goal?

3. What is the future value of a 5-year ordinary annuity that promises to pay you \$300 each year? The rate of interest is 7 percent.

4. What is the future value of a 5-year annuity due that promises to pay you \$300 each year? Assume that all payments are reinvested at 7 percent a year, until Year 5.

#### Solution Preview

Time Value Analysis
1. If you deposit money today into an account that pays 6.5 percent interest, how long will it take for you to double your money?

FV = PV (1+i)n where PV is the present value
i is the interest rate
n is the period

2 = 1 (1.065)n
2 = (1.065)n
n LN(1.065) = LN(2)
n(0.063) = 0.69
n = 11.01

2. John Roberts has \$42,180.53 in a brokerage account, and he plans to contribute an additional \$5,000 to the account at the end of every year. The brokerage account has ...

#### Solution Summary

This solution is comprised of a detailed explanation and calculation to answer the time value of money problems.

\$2.19