Jari invests in a CD with an annual interest rate of 5.45% compounded quarterly. How many years will it take for Jari's investment to double. Round your answer 4 decimal places and include a label (written in lowercase)
Answers
It will take 12.8047 years for Jari's investment to double
Step-by-step explanation:
The formula for compound interest, including principal sum is
, where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount (the initial deposit or loan amount)
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per unit t
- t is the time the money is invested or borrowed for
Jari invests in a CD with an annual interest rate of 5.45% compounded quarterly. We need to find how many years it will take for Jari's investment to double.
∵ The annual interest rate is 5.45%
∴ r = 5.45% = 5.45 ÷ 100 = 0.0545
∵ The interest rate is compounded quarterly
∴ n = 4
∵ The Jari's investment is doubled in t years
∴ A = 2P
- Substitute these values in the rule above
∵
- Divide both sides by P
∴
∴
∴
- Insert ㏒ to both sides
∴
- Remember
∴ ㏒(2) = 4t ㏒(1.013625)
- Divide both sides by 4 ㏒(1.013625) to find t
∴ t = 12.8047 years
It will take 12.8047 years for Jari's investment to double
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