Question

how long will it take money to double if it is invested at the following rates? A) 5.5% compounded semiannually 3) 5.6% compounded semiannually A) years Round to two decimal places as needed.) How long will it take money to double if it is invested at (A) 12% compounded continuously? (B) 14% compounded continuously? (A) At 12% compounded continuously, the investment doubles in years. (Round to one decimal place as needed.) How long will it take money to triple if it is invested at 9% compounded semiannually? 8.7% compounded continuously? It will take about years at 9% compounded semiannually. (Round to two decimal places as needed.) What annual nominal rate compounded semiannually has the same annual percentage yield as 8% compounded continuously? The annual nominal rate is %. (Round to two decimal places as needed.) If you pay $8,450 for a 20 -year zero coupon bond with a face value of $44,000, what is your annual compound rate of return? Annual compound rate =% (Round to two decimal places.)

Answer 1

The time to double or triple an investment through compound interest depends on the compounding frequency and interest rate. Specific formulas involving logarithms are used to calculate the required time for semiannual and continuous compounding. The equivalent semiannual rate for continuous compounding and compound rate of return on a bond can also be calculated using these formulas.

Step-by-step explanation:

The time it takes for money to double or triple with compound interest can be calculated using the formula for compound interest and logarithms. For example, to find out how long it takes to double an investment with a semiannual compound interest rate, you can use the rule of 72 by dividing 72 by the annual interest rate. To calculate the exact time, you could use the formula t = ln(2) / (n * ln(1 + r/n)), where t is the time in years, n is the number of compounding periods per year, and r is the annual interest rate. For continuous compounding, the formula t = ln(2) / r is used. To calculate the equivalent semiannual rate for a continuously compounded rate, you can equate the effective annual rates and solve for the nominal semiannual rate.

For the annual compound rate of return on a zero coupon bond, you can use the formula (Face Value / Purchase Price)^(1/t) - 1, where t is the number of years until maturity.