Question

To the closest year, how long will it take $200 to double if it is deposited and earns the following rates? [Notes: (1) If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can “override” the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. (2) This problem cannot be solved exactly with some financial calculators. For example, if you enter PV = -200, PMT = 0, FV = 400, and I = 7 in an HP-12C and then press the N key, you will get 11 years. The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up. However, the HP10BII gives the exact answer.] Do not round intermediate calculations. Round your answers to the nearest whole number.

1. 7%.

   ------ year(s)

2. 10%.

   -------- year(s)

3. 18%.

   ----------year(s)

4. 100%.

   ----------year(s)

Answer 1

According to the question, $ 200 should become $ 400

If $200 is deposited at 7% , no. of years it will take to double (i.e to become $400) is 10 years.
Working:

400 = 200*(1.07)^n

n = log2/log1.07

= 10.245

= 10 years ..(rounded upto whole no,)

If $200 is deposited at 10% no. of years it will take to double (i.e to become $400) is 7 years

Working:

400 = 200*(1.108)^n

n = log2/log1.10

= 7.273 years

= 7 years ..(rounded upto whole no,)

If $200 is deposited at 18% no. of years it will take to double (i.e to become $400) is 4 years

Working:

400 = 200*(1.18)^n

n = log2/log1.18

= 4.188 years

= 4 years

.

If $200 is deposited at 100% no. of years it will take to double (i.e to become $400) is 1 years

Working:

400 = 200*(2)^n

n = log2/log2

= 1 year