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Loan Amortisation

The Effect of Different Rates of Interest

Here you can see how a loan of 1000.00 (any currency) is repaid over a period of 5 years at different yearly interest rates, if the yearly interest is added to the capital at the end of each year, as it would be in a bank loan or mortgage.

Computation of Growth of 1000.00 at 5% p.a. Computation of Growth of 1000.00 at 10% p.a. Computation of Growth of 1000.00 at 20% p.a. Computation of Growth of 1000.00 at 40% p.a.

Above are the computations of the Payment (PMT), required to repay a loan of 1000.00 (PV) by 30 December 2014, which was taken on 30 December 2009, for 5 years, at different annual (yearly) rates of growth (i%): 5%, 10%, 20%, 40%.

The computations were performed using TimeMoney, an iPhone App, available from the App Store. See also MoneyGrowth for Android devices.

Schedule of Growth of 1000.00 at 5% p.a. Schedule of Growth of 1000.00 at 10% p.a. Schedule of Growth of 1000.00 at 20% p.a. Schedule of Growth of 1000.00 at 40% p.a.

Above are the loan amortisation schedules of the above computations.

The schedules show the reduction of the capital owed within each of the 5 years (compounding periods).

The schedules were produced using TimeMoney, an iPhone App, available from the App Store. See also MoneyGrowth for Android devices.

Graph of Growth of 1000.00 at 5% p.a. Graph of Growth of 1000.00 at 10% p.a. Graph of Growth of 1000.00 at 20% p.a. Graph of Growth of 1000.00 at 40% p.a.

Above are the graphs of the above computations.

The graphs show the reduction of the capital within each of the 5 years (compounding periods).

The green line in the graphs is the Capital (PV). The red line is the total Interest paid at the end of each period. The blue line is the total paid.

Looking at the graphs side by side, one can see that with the increase of the growth rate the part of the payment due to interest (under the red line) becomes progressively greater than the part of the payment due to capital (between the red line and the blue line).

Thus at 5% interest rate the total amount of interest paid is 15.49% of the amount of the loan, while at 40% interest the total amount of interest paid is 145.68% of the amount of the loan. That is, total interest paid is nearly 1.5 times greater than the amount of the loan.

The graphs were produced using TimeMoney, an iPhone App, available from the App Store. See also MoneyGrowth for Android devices.

The formula for Loan (Mortgage) Payment (PMT) is:

PMT = PV * r / (1 - (1 + r) -n)

Where:

PV is Present Value,
r is the yearly interest, as a fraction ( i / 100)
n is number of years.

But with TimeMoney, an iPhone App, available from the App Store, to enter a computation data, or change it, and to produce schedules and graphs is just a few tap on the iPhone screen. See also MoneyGrowth for Android devices.

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