you want to retire in 35 years you currently have 20000 save

you want to retire in 35 years, you currently have $20,000 saved and will like to have $42,000 saved at retirement. what annual interest rate must you earn to reach that goal? Please show work

Solution

t = 35
P = 20000
A = 42000

Annual, so n = 1

A = P(1 + r/n)^(nt)

42000 = 20000(1 + r/1)^(1*35)

2.1 = (1 + r)^35

ln(2.1) = 35 * ln(1 + r)

ln(2.1) / 35 = ln(1 + r)

0.0211982098494108 = ln(1 + r)

e^0.0211982098494108 = 1 + r

1.0214244879683734 = 1 + r

r = 0.0214244879683734

r = 0.0214244879683734*100

r = 2.14% approx ---> answer