Question

You plan to invest $2,000 today in a mutual fund that earns 6% annually for 5 years. Which of the following statements is TRUE?

Select one:

a. All else being equal, if the interest rate doubles, the future value doubles.

b. All else being equal, if the number of periods doubles, the future value doubles.

c. All else being equal, if both the interest rate and the number of periods double, the future value doubles.

d. All else being equal, if the initial investment doubles, the future value doubles.

Answer 1

Answer-

Initial investment = PV = $ 2000
Interest rate = I/Y = 6 %
Number of Years or periods = N = 5
Payments = $ 0

Future Value = FV = ?

By substituting the values in financial calculator we get

Future Value = FV = $ 2676.45

Lets evaluate all the Scenarios

a.

If the interest rate doubles the future value doubles

Interest rate doubles = I/Y = 2 x 6 % = 12 %
Keeping all other values similar we get

Future value = $ 3524.68

The Future value did not double as $ 2676.45 x 2 = $ 5352.9

This Option is not True

b.

If the number of periods doubles, the future value doubles

Number of period doubles = N = 2 x 5 = 10
Keeping all other values similar we get

Future value = $ 3581.69

The Future value did not double as $ 2676.45 x 2 = $ 5352.9

This Option is not True

c.

If both the interest rate and the number of periods double, the future value doubles.

Interest rate doubles = I/Y = 2 x 6 % = 12 %
Number of periods double = N = 2 x 5 = 10

Keeping all other values similar we get

Future value = $ 6211.69

The future value is more than double as $ 2676.45 x 2 = $ 5352.9 < $ 6211.69

This Option is not True

d.

if the initial investment doubles, the future value doubles

Initial investment doubles = 2 x $ 2000 = $ 4000
Keeping all other values similar we get

Future value = $ 5352.9

The future value is exactly double = $ 2676.45 x 2 = $ 5352.9 is equal to the above calculated value.

This Option is True

Therefore Option d is True. Options A,B and C are False.

Note - In all the Options the given condition is applied and all other variables are kept same and the Future value is calculated.