FIN2603 – Finance for Non-Financial Managers (2023)
Study Unit 05: The time value of money (PB: Chapter 5)
The timing of cash flows has important economic consequences because firms and individuals have
many opportunities to earn positive rates of return on invested funds.
• Future value (FV), the value of a present amount at a future date, is calculated by applying
compound interest over a specific period.
• Present value (PV) represents the rand value today of a future amount, or the amount you
would invest today at a given interest rate for a specified period to equal the future amount.
❖ Time value of money - an amount of money invested today, is worth more than it will be at
some point in time in the future.
❖ Opportunity cost - if you are expecting to receive an amount of money in the future, an
opportunity cost is involved in waiting to receive the amount.
❖ Inflation - refers to a continuous rise in the general level of prices of goods and services.
1. Future value:
Future value is the calculation of interest on a present amount to get some future amount.
The amount on which interest is paid is known as the principal. Future value is the amount to
which the principal will grow by a given future date when compounded at a certain interest
rate.
The three types of compounding are as follows:
• annual compounding
• intra-year compounding
• the future value of an annuity
The general formula that can be used to calculate the FV is as follows:
FVn = PV (1 + i)ⁿ
FVn = the future value of the amount at the end of n periods
PV = the initial principal
i = the annual rate of interest paid
n = the number of periods of the investment
1. Annual compounding - Interest is compounded when the amount earned on the initial
principal becomes part of the principal at the end of the first compounding period.
EXAMPLE
If an investor places R IO 000 in a savings account paying 10% interest compounded annually, then at
the end of the first year he or she will have earned R I 000 in interest. The value of his or her investment
will be R I I 000; R IO 000 representing the initial principal and R I 000 in interest. The future value at the
end of the first year is calculated as follows:
Lyana Petzer Page 1 of 21
, FIN2603 – Finance for Non-Financial Managers (2023)
Future value at the end of year 1 = R 10 000 (I + 0.10)
= R 11 000
The calculation can also be done using a financial calculator (HP I 0B11):
Key in: Press: Calculator display Notes
- 10 000 → PV - 10 000 Stands for present value
10 → I/YR 10 Indicates the interest rate
1 → N 1 Indicates the number of periods
→ FV 11 000 Determines future value
Future value at the end of year 2 = R 10 000 (I + 0.10) (I + 0.10)
= R 10 000 (I + 0.10) ²
= R 12 000 x 1.2I
= R 12 100
The calculation can also be done using a financial calculator (HP I 0B11):
Key in: Press: Calculator display Notes
- 10 000 → PV - 10 000 Stands for present value
10 → I/YR 10 Indicates the interest rate
2 → N 2 Indicates the number of periods
→ FV 12 100 Determines future value
Lyana Petzer Page 2 of 21
, FIN2603 – Finance for Non-Financial Managers (2023)
2. Intra-year compounding - interest is compounded more often than once a year. Savings
institutions compound interest semi-annually, quarterly, monthly, weekly or daily. It
changes the frequency with which the interest is calculated, and this requires adjustments to
the number of periods(n) and the interest payable(i).
Compounding during Adjustment to Adjustment to Explanation
a 1-year period number of periods interest rate
Semi-annual N×2 i÷2 Instead of the nominal interest
rate being paid once a year, one-
half of the interest rate is paid
twice a year.
Quarterly N×4 i÷4 Instead of the nominal interest
rate being paid once a year, one
quarter of the interest rate is paid
four times a year.
Monthly N × 12 i ÷ 12 Instead of the nominal interest
rate being paid once a year, one
twelfth of the interest rate is paid
twelve times a year.
Weekly N × 52 i ÷ 52 Instead of the nominal interest
rate being paid once a year, one
fifty second part of the interest
rate is paid fifty-two times per
year.
Daily N × 365 i ÷ 365 Instead of the nominal interest
rate being paid once a year, one
three hundred-and-sixty-fifth part
of the interest rate is paid three
Lyana Petzer Page 3 of 21
Study Unit 05: The time value of money (PB: Chapter 5)
The timing of cash flows has important economic consequences because firms and individuals have
many opportunities to earn positive rates of return on invested funds.
• Future value (FV), the value of a present amount at a future date, is calculated by applying
compound interest over a specific period.
• Present value (PV) represents the rand value today of a future amount, or the amount you
would invest today at a given interest rate for a specified period to equal the future amount.
❖ Time value of money - an amount of money invested today, is worth more than it will be at
some point in time in the future.
❖ Opportunity cost - if you are expecting to receive an amount of money in the future, an
opportunity cost is involved in waiting to receive the amount.
❖ Inflation - refers to a continuous rise in the general level of prices of goods and services.
1. Future value:
Future value is the calculation of interest on a present amount to get some future amount.
The amount on which interest is paid is known as the principal. Future value is the amount to
which the principal will grow by a given future date when compounded at a certain interest
rate.
The three types of compounding are as follows:
• annual compounding
• intra-year compounding
• the future value of an annuity
The general formula that can be used to calculate the FV is as follows:
FVn = PV (1 + i)ⁿ
FVn = the future value of the amount at the end of n periods
PV = the initial principal
i = the annual rate of interest paid
n = the number of periods of the investment
1. Annual compounding - Interest is compounded when the amount earned on the initial
principal becomes part of the principal at the end of the first compounding period.
EXAMPLE
If an investor places R IO 000 in a savings account paying 10% interest compounded annually, then at
the end of the first year he or she will have earned R I 000 in interest. The value of his or her investment
will be R I I 000; R IO 000 representing the initial principal and R I 000 in interest. The future value at the
end of the first year is calculated as follows:
Lyana Petzer Page 1 of 21
, FIN2603 – Finance for Non-Financial Managers (2023)
Future value at the end of year 1 = R 10 000 (I + 0.10)
= R 11 000
The calculation can also be done using a financial calculator (HP I 0B11):
Key in: Press: Calculator display Notes
- 10 000 → PV - 10 000 Stands for present value
10 → I/YR 10 Indicates the interest rate
1 → N 1 Indicates the number of periods
→ FV 11 000 Determines future value
Future value at the end of year 2 = R 10 000 (I + 0.10) (I + 0.10)
= R 10 000 (I + 0.10) ²
= R 12 000 x 1.2I
= R 12 100
The calculation can also be done using a financial calculator (HP I 0B11):
Key in: Press: Calculator display Notes
- 10 000 → PV - 10 000 Stands for present value
10 → I/YR 10 Indicates the interest rate
2 → N 2 Indicates the number of periods
→ FV 12 100 Determines future value
Lyana Petzer Page 2 of 21
, FIN2603 – Finance for Non-Financial Managers (2023)
2. Intra-year compounding - interest is compounded more often than once a year. Savings
institutions compound interest semi-annually, quarterly, monthly, weekly or daily. It
changes the frequency with which the interest is calculated, and this requires adjustments to
the number of periods(n) and the interest payable(i).
Compounding during Adjustment to Adjustment to Explanation
a 1-year period number of periods interest rate
Semi-annual N×2 i÷2 Instead of the nominal interest
rate being paid once a year, one-
half of the interest rate is paid
twice a year.
Quarterly N×4 i÷4 Instead of the nominal interest
rate being paid once a year, one
quarter of the interest rate is paid
four times a year.
Monthly N × 12 i ÷ 12 Instead of the nominal interest
rate being paid once a year, one
twelfth of the interest rate is paid
twelve times a year.
Weekly N × 52 i ÷ 52 Instead of the nominal interest
rate being paid once a year, one
fifty second part of the interest
rate is paid fifty-two times per
year.
Daily N × 365 i ÷ 365 Instead of the nominal interest
rate being paid once a year, one
three hundred-and-sixty-fifth part
of the interest rate is paid three
Lyana Petzer Page 3 of 21
