Question

If $500 is put into a savings account at 9% interest compounded continuously, how much will it be worth at the end of 3 years? How many years will it take to double in value?

Answer 1

$654.98

Around 7.7 years

Explanation:

Value = P × e^(rt)

= 500 × e^(0.09×3)

= 500 × e^(0.27)

= 654.9822254

Double: 500 × 2 = 1000

1000 = 500 × e^(0.09t)

e^(0.09t) = 2

Use ln both sides

0.09t × lne = ln2

t = ln2 ÷ 0.09

t = 7.70163543