Question

How long will it take $700 to double if it earns the following rates? Compounding occurs once a year. Round your answers to two decimal places.

1. 7%.

   year(s)

2. 11%.

   year(s)

3. 18%.

   year(s)

4. 100%.

   year(s)

Answer 1

The Principal is $700

Interest Rate

Part -A) Interest rate is 7%

Amount = Principal + Interest

Amount has to be doubled so it will become $1400.

Compound Interest = Principal * ( 1 + Rate ) ^ Number of Years

1400 = 700 * ( 1 + 7%)^ N

1400/700 = (1.07)^N

2 = (1.07)^N

By using trial and error method,

2 = (1.07)^10.20

So, It will take 10.2 years to double the amount at 7% interest rate.

2.  

Interest rate is 11%

Amount = Principal + Interest

Amount has to be doubled so it will become $1400.

Compound Interest = Principal * ( 1 + Rate ) ^ Number of Years

1400 = 700 * ( 1 + 11%)^ N

1400/700 = (1.11)^N

2 = (1.11)^N

By using trial and error method,

2 = (1.11)^6.66

So, It will take 6.66 years to double the amount at 11% interest rate.

3.

Interest rate is 18%

Amount = Principal + Interest

Amount has to be doubled so it will become $1400.

Compound Interest = Principal * ( 1 + Rate ) ^ Number of Years

1400 = 700 * ( 1 + 18%)^ N

1400/700 = (1.18)^N

2 = (1.18)^N

By using trial and error method,

2 = (1.18)^4.20

So, It will take 4.20 years to double the amount at 18% interest rate.

4.

Interest rate is 100%

Amount = Principal + Interest

Amount has to be doubled so it will become $1400.

Compound Interest = Principal * ( 1 + Rate ) ^ Number of Years

1400 = 700 * ( 1 + 100%)^ N

1400/700 = (2)^N

2 = (2)^N

By using trial and error method,

2 = (2)^1

So, It will take 1 years to double the amount at 100% interest rate.