At 7.25 percent interest, how long does it take to double your money?

Requirement 1:

At 7.25 percent interest, how long does it take to double your money? (Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Length of time

years

Requirement 2:

At 7.25 percent interest, how long does it take to quadruple your money? (Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Length of time

years

rev: 04-29-2011

Explanation:

To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)t

Solving for t, we get:

t = ln(FV / PV) / ln(1 + r)

1:

The length of time to double your money is:

FV = $2 = $1(1.0725)t

t = ln 2 / ln 1.0725

t = 9.90 years

2:

The length of time to quadruple your money is:

FV = $4 = $1(1.0725)t

t = ln 4 / ln 1.0725

t = 19.81 years

Notice that the length of time to quadruple your money is twice as long as the time needed to double your money (the slight difference in these answers is due to rounding). This is an important concept of time value of money.

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

7.25%

±$1

$2

N

I/Y

PV

PMT

FV

Solve for

9.90

Enter

7.25%

±$1

$4

N

I/Y

PV

PMT

FV

Solve for

19.81