If you open a savings account that earns 7.5% simple interest per year, what is the minimum number of years you must wait to double your balance? Suppose you open another account that earns 7% interest compounded yearly. How many years will it take now to double your balance?

Case 1 = 13.33 years

Case 2 = 10.25 years

Explanation:

Case 1

Interest rate = 7.5% = 0.075

Future value = 2 * Present value

Now,

Future value = Present value * [ 1 + (Rate * Time) ]

or

2 * Present value = Present value * [ 1 + (0.075 * Time) ]

or

2 = 1 + (0.075 * Time)

or

1 = 0.075 * Time

or

Time = 13.33 years

Case 2

Interest rate, r = 7% = 0.07

Future value = 2 * Present value

Now,

Future value = Present value * (1 + r) ⁿ

here,

n is the time

thus,

2 * Present value = Present value * (1 + 0.07) ⁿ

or

2 = 1.07ⁿ

taking log both the sides

log (2) = log (1.07ⁿ)

also,

log (aᵇ) = b * log (a)

thus,

log (2) = n * log (1.07)

or

0.301 = n * 0.02938

or

n = 10.25 years