Finance Basics for Managers: Time Value of Money Problems
FIN2110 Finance Basics for Managers Fall 2011
Time Value of Money Problems
Calculating Future Values
Assume you deposit $10,000 today in an account that pays 6% interest. How much will you have in five years?
= $10,000 (FVIF of 6%, 5years)
= $10,000 * 1.3382
= $13,382
Calculating Present Values
Suppose you have just celebrated your 19th birthday. A rich uncle has set up a trust fund for you that will pay you $150,000 when you turn 30. If the relevant discount rate is 9%, how much is the fund worth today?
We know,
Present Value = Future Cash Flow / (1 + Required Rate of Return) ^Number of Years You Have To Wait For The Cash Flow
Given,
Present value = $150,000 / (1 + .09) ^ 11
= $150,000 / 2.5804
= $ 58,130
Therefore,
The present value is thus about $58,130.
Calculating Rates of Return
You’ve been offered an investment that will double your money in 10 years. What rate of return are you being offered? Use the Rule of 72 to calculate the answer.
Suppose, we spend $1,000, than according the question the money will be double in 10 years which will $2,000. So,
Present value = $1,000
Future Value = $2,000
Time = $ 10 year
$2,000 = $1,000 * (1 + r)^10
2 = (1 + r) ^10
2(1/10) = 1 + r
r = 7.18%
For each of the following, compute the future value:
Present Value Years Interest Rate Future Value
$2,250 11 10% $6419.51
$8,742 7 8% $14,982.25
$76,355 14 17% $687,764.17
$183,796 8 7% $315,795.75
For each of the following, compute the present value:
Present Value Years Interest Rate Future Value
$10,295.65 6 7% $15,451
$21,914.85 7 13% $51,557
$43,516.90 23 14% $886,073
$116,631.32 18 9%
Time Value of Money Problems
Calculating Future Values
Assume you deposit $10,000 today in an account that pays 6% interest. How much will you have in five years?
= $10,000 (FVIF of 6%, 5years)
= $10,000 * 1.3382
= $13,382
Calculating Present Values
Suppose you have just celebrated your 19th birthday. A rich uncle has set up a trust fund for you that will pay you $150,000 when you turn 30. If the relevant discount rate is 9%, how much is the fund worth today?
We know,
Present Value = Future Cash Flow / (1 + Required Rate of Return) ^Number of Years You Have To Wait For The Cash Flow
Given,
Present value = $150,000 / (1 + .09) ^ 11
= $150,000 / 2.5804
= $ 58,130
Therefore,
The present value is thus about $58,130.
Calculating Rates of Return
You’ve been offered an investment that will double your money in 10 years. What rate of return are you being offered? Use the Rule of 72 to calculate the answer.
Suppose, we spend $1,000, than according the question the money will be double in 10 years which will $2,000. So,
Present value = $1,000
Future Value = $2,000
Time = $ 10 year
$2,000 = $1,000 * (1 + r)^10
2 = (1 + r) ^10
2(1/10) = 1 + r
r = 7.18%
For each of the following, compute the future value:
Present Value Years Interest Rate Future Value
$2,250 11 10% $6419.51
$8,742 7 8% $14,982.25
$76,355 14 17% $687,764.17
$183,796 8 7% $315,795.75
For each of the following, compute the present value:
Present Value Years Interest Rate Future Value
$10,295.65 6 7% $15,451
$21,914.85 7 13% $51,557
$43,516.90 23 14% $886,073
$116,631.32 18 9%