Example Financial Calculations

Compounding Interest - Time Value of Money
Simple Interest Calculations
Amortization
Discounted Cash-Flows
Depreciation
Continuous Compounding Periods

Compounding Interest - Time Value of Money

Effective Annual Rate of Interest

1. Calculate the Effective Annual Rate of interest, if interest is compounded at 0.5% per month.

[SHIFT] [CLREG] (clears the TVM registers)
{0.5} [i]
{12} [n]
{100} [+/-] [PV]
[FV] [-] {100} [=] gives result 6.17%

Payments in Arrears

For these examples, ensure that the calculator is in the END (payments in arrears) mode by using the [BEG/END] button (i.e. the 'BEGIN' indicator should not be visible in the display). In this mode, payments or receipts are made at the end of a payment period.

2. Suppose that you have $2,000 today and can invest this at 12% APR over the next 5 years with a quarterly compounding interest. Determine the value of the investment after 5 years.

[SHIFT] [BEG/END] (set END mode if appropriate)
{2,000} [+/-] [PV] (stores -1,000 in the PV register)
{5} [×] {4} [=] 20 [n] (stores 5 years of quarterly periods in the n register)
{12} [÷] {4} [=] 3 [i] (stores the quarterly interest rate in i register)
{0} [PMT] (no further payments)
[FV] gives result $3612.22

3. You expect to receive 10,000 Euros in 6 years time from a savings account with an annually compounding interest rate of 7.5%. What is the balance today?

[SHIFT] [CLREG] (clears the TVM registers)
{6} [n] (stores 6 years in the n register)
{10,000} [FV] (stores 10,000 in the FV register)
{7.5} [i] (stores 7.5% in the i register)
[PV] gives -6479.612

Note that the negative result is due to the cash-flow sign convention. See the financial introduction for more information.

4. What annual interest rate must be obtained to accumulate $100,000 in 15 years on an investment of $40,000 with semi-annual compounding?

[SHIFT] [CLREG] (clears the TVM registers)
{15} [×] {2} [=] [n] (total of 30 semi-annual periods)
{100,000} [FV] (stores 100,000 in FV)
{60,000} [+/-] [PV] (stores -60,000 in PV)
[i] returns 3.10 (semi-annual interest rate)
[×] {2} [=] 6.20 (annual interest rate)

5. You're planning to purchase a new car. Your bank offers you a $20,000 loan at 9.5% interest. If you make $250 payments at the end of each month, how many payments will be required to pay off the loan?

{20,000} [PV] (you receive $20,000 now)
{9.5} [SHIFT] [12÷] (stores 9.5 / 12 in the i register)
{250} [+/-] [PMT] (stores -250, i.e. you pay out $250 each period)
{0} [FV] (when the loan is paid, the future value will be zero)
[n] gives the result 127.23 (127 full payments and a final payment of 0.23 x 250 = 58.47)

Annuity Due

6. For annuities due, payments in advance, payments or receipts are at the beginning of a payment period. In such cases, you should set your calculator to BEGIN mode by pressing [SHIFT] [BEG/END]. This will affect the results of your calculations because interest will be accrued over longer periods than in END mode.

You will receive $150 per month for the next 5 years. If the appropriate annual interest rate is 8%, what are your accumulated funds at the end of three years?

[SHIFT] [BEG/END] (set BEGIN mode if appropriate)
{5} [SHIFT] [12×] (stores 60 periods in n registers)
{0} [PV] (nothing today)
{150} [PMT] (you receive payments of 150 each period)
{8} [12÷] (periodic interest stored in i register)
[FV] gives -11095.00

Simple Interest Calculations

7. Your friend asks you for a loan of 4,000 GBP to start her own company, and agrees to pay you back in 150 days at a 6% simple interest rate to be calculated on a 360-day basis. What is the amount of accrued interest she will owe you in 150 days, and what is the total amount owed?

{150} [n] (stores 150 days)
{6} [i] (stores interest rate)
{450} [+/-] [PV] (stores principal amount)
[SHIFT] [INT] gives result 11.25 (360-day basis)
[+] [RCL] [PV] [+/-] [=] 461.25 (add this to principal amount recalled from PV register)

8. Same as above, but this time for interest calculated on a 365-day basis.

{150} [n] (stores 150 days)
{6} [i] (stores interest rate)
{450} [+/-] [PV] (stores principal amount)
[SHIFT] [INT] gives 11.25 (360-day basis)
[X<>Y] gives 11.10 (retrieves 365-day result from y register)
[+] [RCL] [PV] [+/-] [=] 461.25 (add this to principal amount recalled from PV register)

Amortization

9. Your bank offers you a loan of $15,000 at an annual rate of 9.5% over 10 years, compounded monthly. In the first year, how much of the principal balance will you have paid off, how much interest will you have paid and what will be the remaining balance?

Step 1. Enter this information into the TVM registers and calculate the payment:

[BEG/END] (set to END mode if necessary)
{10} [SHIFT] [12×]
{9.5} [SHIFT] [12÷]
{15,000} [PV]
{0} [FV]
[PMT] payment calculation, giving result -194.10

Step 2. Amortize for the first 12 months:

{12} [AMORT] gives result -1384.57 (the interest paid in first year)
[X<>Y] gives result -944.63 (retrieves the principal paid from the y register)
[RCL] [PV] gives 14055.37 (the remaining balance)

10. How much will be paid in interest on the loan above over the remaining 9 year period?

{12} [×] {9} [=] [AMORT] gives -6906.70 (remaining total interest to be paid)

Hence, the total interest paid over the lifetime of the loan is $6906.70 + $1384.57 = $5522.13.

Discounted Cash-Flows

11. A project has the following expected cash-flow and the firm's cost of capital is 8%. What is the Net Present Value (NPR)?

CF(n) = -60000, -1000, 3500, 2500, 4500, 80000

Enter this cash-flow, either by using the Numeric Data List Window, or the [CF0] and [CFj] keys on the calculator.

Now key in:

{8} [i] (stores interest rate)
[NPV] gives result 1813.63

12. What is the Internal Rate of Return (IRR) for the project described in the example above?

With the above cash-flow unchanged, press:

[IRR] to give 8.67

Depreciation Calculations

13. You buy a new computer, costing 2,000 Euros, for your business. You, somewhat hopefully, plan to get five years of life out of it and sell it for scrap for 50 Euros afterwards. What is amount of depreciation, based on the straight-line (SL) method, after two years, and what is the remaining depreciable balance?

{2,000} [PV] (initial cost)
{5} [n] (useful life in years)
{50} [FV] (salvage value)
{2} [SHIFT] [SL] gives result 390 (amount of depreciation in year 2)
[X<>Y] gives 1,170 (remaining depreciable balance)

14. Same problem as above, but using the sum of digit years (SOYD) method:

{2,000} [PV] (initial cost)
{5} [n] (useful life in years)
{50} [FV] (salvage value)
{2} [SHIFT] [SOYD] gives result 520 (amount of depreciation in year 2)
[X<>Y] gives 780 (remaining depreciable balance)

15. Same problem, but using the declining balance DB method, with a declining balance factor of 1.25:

{2,000} [PV] (initial cost)
{5} [n] (useful life in years)
{50} [FV] (salvage value)
{125} [i] (1.25 declining balance factor as a percentage value)
{2} [SHIFT] [DB] gives result 375 (amount of depreciation in year 2)
[X<>Y] gives 1,075 (remaining depreciable balance)

Continuous Compounding Periods

If compounding periods are continuous, it means that the time between them is considered to be infinitesimally small, hence they are continuously compounding. In this case, to calculate future FV and present PV values, use the following formulas:

FV = PV × e^rn

PV = FV × e^-rn

where:

e is the natural number, i.e. 2.7182...
r is periodic interest rate as a decimal value (not as a percentage)
n is the number periods

16. Example. You have invested $2,000 dollars in a venture which offers an annual continuously compounded return of 5%. How much will the investment be worth in 6 months?

In the DreamCalc standard order input mode, key in:

{2,000} [×] [(--] {0.05} [×] {0.5} [--)] [e^x] [=] 2,050.63

In true order mode, enter:

{2,000} [×] [e^x] [(--] {0.05} [×] {0.5} [--)] [=] 2,050.63