erma93
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You borrow £150,000 from a bank to buy a flat. The effective rate of interest is 7% per
annum. The loan has term 25 years and is to be repaid by monthly repayments paid in
arrears. The amount of each repayment during the first two years is half of the amount
of each repayment thereafter.
1. Calculate the amount of the first repayment.
2. Calculate the total amount of interest paid to the bank.
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Doctor_Einstein
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(Original post by erma93)
You borrow £150,000 from a bank to buy a flat. The effective rate of interest is 7% per
annum. The loan has term 25 years and is to be repaid by monthly repayments paid in
arrears. The amount of each repayment during the first two years is half of the amount
of each repayment thereafter.
1. Calculate the amount of the first repayment.
2. Calculate the total amount of interest paid to the bank.
The present value of an ordinary annuity (paid in arrears), is given by:

PV = C*[1-(1+i)^(-n)]/i, where C is the cash flow in each period, i is the interest rate over the period and n is the number of periods.

You're effective interest rate is 7%, and therefore it is permissible to deal with n in years, and i as the effective interest rate.

You have two cash flows in your scenario:

(1)The first cash flow is over 2 years with monthly repayments given by a constant say C. The present value of this cash flow is therefore:

PV = C*[1-(1+i)^(-2)]/i

(2) The second cash flow is over 23 years with monthly repayments given by 2*C. We also must discount the cash flow back by a further 2 years to get the present value 2 years prior to the beginning of this cash flow which is the present time. That is,

PV = [(1+i)^-2]*2C*[1-(1+i)^(-23)]/i

----------------

The present value of both cash flows, which should be 150,000 is therefore:

150,000 = C*[1-(1+i)^(-2)]/i + [(1+i)^-2]*2C*[1-(1+i)^(-23)]/i

where i = 0.07 and C is unknown.

By solving the above equation for C, you have determined your initial repayment amount.

To calculate the total interest, simply evaluate 2C + 23*2C and subtract 150,000 from this amount.
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