Question

How many years will it take an account to double in value, assuming a 5.2% interest rate compounded quarterly? Round your answer to the nearest tenth.​

Answer 1

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years.

How to determine the doubling time of money account

The compound interest takes into account the change of money deposited in time in contrast with the simple interest, which only takes the initial amount of money into account. Please notice that four quarters equals a year.

The compound interest formula is described below:

C = C' · (1 + r/100)ⁿ     (1)

Where:

• r - Interest rate
• n - Number of periods
• C' - Initial money amount
• C - Current money amount

If we know that C = 2 · C' and r = 5.2, then the doubling time is:

n = /㏒ C/C'/㏒ (1 + r/100)

n = ㏒ 2/㏒ 1.052

n ≈ 13.674

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years. $\blacksquare$

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