Question

Your parents will retire in 15 years. They currently have $250,000 saved, and they think they will need $1,550,000 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.

What is the present value of a security that will pay $26,000 in 20 years if securities of equal risk pay 6% annually? Do not round intermediate calculations. Round your answer to the nearest cent.

If you deposit $6,000 in a bank account that pays 9% interest annually, how much will be in your account after 5 years? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

1. FV = 1,550,000

PV = 250,000

n = 15

FV = PV * (1 + r)^n

(1 + r)^n = FV/PV

(1 + r) = (FV/PV)^(1/n)

1 + r = (FV/PV)^(1/n) - 1

r = (FV/PV)^(1/n) - 1

r = (1,550,000/250,000)^(1/15) - 1

r = 0.1293436457

r = 12.93%

They should earn an annual interest rate of 12.93%

2. PV = FV/(1 + r)^n

PV = 26,000/(1 + 0.06)^20

PV = $8,106.9228990382

The present value = $8,106.92

3. FV = PV * (1 + r)^n

FV = 6,000 * (1 + 0.09)^5

FV = $9,231.7437294

We would have $9,231.74 in our account after 5 years