Question

1. What’s the future value of $500 after 3 years if it earns 8%, annual compounding?
2. What’s the present value of $500 to be received in 3 years if the interest rate is 8%, annual compounding?
3. What annual interest rate would cause $1,000 to grow to $2,000 in 8 years?

Answer 1

1. Future value of $500 after 3 years & earns 8%, annual compounding

FV = PV x (1 + R)^N

PV = Money invested today R = Annual rate of interest N = Number of years

FV = $500 x (1 + 8%)³ = $500 x (1 + 0.08)³  = $500 x 1.08³ = $500 x 1.259712 = $629.856

FV = $629.86

2. Present value of $500 to be received in 3 years & interest rate is 8%, annual compounding

PV = FV / (1 + R)^N = $500 / (1 + 8%)³ = 500 / 1.08³ = $500 / 1.259712 = $396.916

PV = $396.92

3. Annual interest rate would cause $1,000 to grow to $2,000 in 8 years

FV = PV x (1 + R)^N

$2,000 = $1,000 x (1 + R)⁸

$2,000 /  $1,000 = (1 + R)⁸

2 = (1 + R)⁸

2^(1/8) = 1 + R

1.0905077 = 1 +R

R = 1.0905077 - 1 = 0.09050 = 9.05%

Annual interest rate = 9.05%