Mortgage Calculator - How the Lenders Work Out Your Payments

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How interest is charged

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How is Mortgage Calculator - How the Lenders Work Out Your Payments

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Mortgage lenders in the United Kingdom use a number of distinct methods for charging interest, these methods fall into one of three categories: -
Daily interest charging. Monthly interest charging. each year interest charging.
Annual interest charging

The most simplest of these is the each year interest charging method, this is indeed the oldest method adopted by lenders. Interest is calculated at the start of the year based on the mortgage equilibrium figure. This interest number is then divided through the 12 months of the year for each cost for an interest-only mortgage or combined with capital for each cost if a full reimbursement mortgage.

Interest-only calculation

Monthly cost = (balance x rate)/12

So with a equilibrium of £100,000 and a rate of 6.5%: -

Monthly cost = (100,000 x 0.065)/12

Monthly cost = £541.67

Full reimbursement calculation

Monthly cost = [[rate x (balance x (1+rate)^term)]/(1-(1+rate)^term) ] / 12

so with a equilibrium of £100,000 and a rate of 6.5%: -

Monthly cost = [[0.065 x (100000 x (1+0.065)^25)]/(1-(1+0.065)^25) ] / 12

Monthly cost = £683.18

Monthly interest charging

With monthly interest charging, the each year interest rate is first divided by 12 to build a monthly interest rate. This new monthly interest rate is then applied to the mortgage equilibrium to presume a monthly interest fee for each cost on an interest-only mortgage or combined with capital for each cost if a full reimbursement mortgage.

Interest-only calculation

Monthly payments = equilibrium x (rate/12)

So with a equilibrium of £100,000 and a rate of 6.5%: -

Monthly payments = 100000 x (0.065/12) Monthly payments = £541.67

Full reimbursement calculation

Monthly pay rate (mrate) = rate/12

Monthly cost = [mrate x (balance x (1 + mrate)^(term x 12)]/[1-(1+mrate)^(term x 12)]

so with a equilibrium of £100,000 and a rate of 6.5%: -

mrate = 0.065/12

Monthly cost = [0.0054 x (100000 x (1 + 0.0054)^300]/[1-(1+0.0054)^300]

Monthly cost = £675.21

As you can see there are benefits to having a monthly interest calculated mortgage over an annually expensed one if your mortgage is a full reimbursement mortgage as this example shows a saving of £8 per month.

Daily interest charging

Many mortgage lenders in the Uk have now adopted daily interest charging methods, this method is far more complex and many lenders have their own rules on how they presume daily charges of interest. Therefore for the purpose of this description the following method will be used, this should provide a guide to how much savings can be made with a daily interest charging method. In order to presume the daily rate of interest we start with the each year interest rate and divide this through by 365.25 days (0.25 being the leap year). We must then multiply this by the days in any particular month. Any way you do not make mortgage payments every particular day so these charges are rolled up and expensed to you on a monthly basis. The main advantage with daily interest charging comes when you make over-payments reducing your mortgage equilibrium immediately benefiting from lower interest being charged. Daily interest charging is often used with flexible mortgages, offset mortgages and current account mortgages as these present huge benefits to the borrower.

Dealing with rate changes

Most of today's mortgages start of with a special offer rate for a period of time then the mortgage often reverts to the lenders acceptable variable rate. For example a 4.5% fixed for 2 years followed by the lenders acceptable variable rate currently 5.6%. How do you presume what payments will be in 2 years time once the special rate period has expired? naturally put you just start over using the new balance, and remaining term. So based on an primary loan number of £100,000 and mortgage term of 25 years

Interest-only mortgage

First mortgage cost = 100000 x (0.045/12)

First mortgage cost = £375.00

then mortgage payments after the first 2 years will increase to: -

First mortgage cost = 100000 x (0.045/12)

First mortgage cost = £375.00

Full reimbursement mortgage

mrate = 0.045/12

First mortgage cost = [0.00375 x (100000 x (1 + 0.00375)^300]/[1-(1+0.00375)^300]

First mortgage cost = £555.83

In order to presume the new mortgage payments after the first 2 years we must first presume the new equilibrium as capital will have been paid for 24 months: -

Future equilibrium = Monthly cost x [(1-(1+mrate^(term x 12)))/mrate]-(-Initial equilibrium x (1+mrate)^(term x 12)

Future equilibrium = 555.83 x [(1-(1+0.00375^300))/0.00375]-(-100000 x (1+0.00375)^300

Future equilibrium = £95467.67

Now we have a equilibrium for 2 years in the future we can start over with a new equilibrium and a 23 year term: -

Next mortgage cost = [0.00467 x (95467.67 x (1 + 0.00467)^276]/[1-(1+0.00467)^276]

Next mortgage cost = £615.91

Lenders will use a similar process to this when a variable rate changes while the term of the mortgage. They will first notify you of the rate change and then presume the equilibrium and start over with the remaining term, equilibrium and new rate.

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