Question

1. Your parents will retire in 26 years. They currently have $340,000 saved, and they think they will need $2,100,000 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. What is the present value of a security that will pay $24,000 in 20 years if securities of equal risk pay 6% annually? Round your answer to the nearest cent.

3. You have $45,055.29 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $260,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations.

Answer 1

1.

FV = PV (1 + r)^n

Where,

Maturity value (FV) = $2100000

Present value (PV) = $340000

Time (n) = 261.072539 = (1 + i)

Lets put all the values in the formula to solve for interst rate (i)

2100000 = 340000 (1 + i) ^26

2100000/ 340000 = (1 + i) ^26

6.1765 = (1 + i) ^26

26√6.1765 = (1 + i)                                                  {Taking 26th root of 6.1765}

1.072539 = (1 + i)

i = 1.072539 - 1

i = 0.07254

So interest rate is 0.0725 or 7.25% per annum

2.

Present value is the present worth of cash that is to be received in the future, if future value is known, rate of interest in r and time is n then PV is

PV = FV/ (1 + r) ^n

Where,

FV = 24000

r = 0.06

n = 20

Let's put all the values in the formula

= 24000/ (1 + 0.06)^20

= 24000/ (1.06)^20

= 24000/ 3.2071

= 7483.4

So PV of the amount is $7483.4