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31 December, 09:45

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?

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  1. 31 December, 11:50
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    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
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