Question

1. Your parents will retire in 27 years. They currently have $320,000 saved, and they think they will need $1,150,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

2. If you deposit money today in an account that pays 14% annual interest, how long will it take to double your money? Round your answer to two decimal places.

3. You have $14,411.29 in a brokerage account, and you plan to deposit an additional $4,000 at the end of every future year until your account totals $200,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number.

4. What's the future value of a 7%, 5-year ordinary annuity that pays $500 each year? If this was an annuity due, what would its future value be? Do not round intermediate calculations. Round your answers to the nearest cent.

Answer 1

Answer 1.

Amount Invested = $320,000
Desired Sum at retirement = $1,150,000
Time to Retirement = 27 years

Let Annual Interest Rate be i%

Amount Invested * (1 + i)^n = Desired Sum
$320,000 * (1 + i)^27 = $1,150,000
(1 + i)^27 = 3.59375
1 + i = 1.0485
i = 0.0485 or 4.85%

So, you need to earn 4.85% on the $320,000 to have $1,150,000 after 27 years.

Answer 2.

Annual Interest Rate = 14%

Let amount invested be $1, desired sum be $2 and n be the number of years to double amount invested.

Amount Invested * (1 + i)^n = Desired Sum
$1 * (1 + 0.14)^n = $2
1.14^n = 2
n * ln(1.14) = ln(2)
n = 5.29 years

So, amount invested will double itself in 5.29 years if interest rate earned is 14%