Question

A. You have just bought an apartment for ¥62 million, using a deposit amounting to ¥8 million, and you borrowed the rest. The loan interest rate is 3.2% p.a compounded monthly and you have taken the loan with a twenty year life. i. Calculate the monthly repayments needed to fully repay the loan within twenty years (assuming repayments occur at the end of the month). ii. After 30 months the interest rate increases to 4.2% p.a. what is the new monthly payment needed now to ensure the loan is still paid of within the twenty years?

Answer 1

1)	The loan amount of Y54,000.000 is the PV of the 240 monthly payments discounted at 3.2% per annum compounded monthly.
	Using the formula for computing PV of an annuity and substituting available figures we have the equation
	54000000 = A*((1+0.032/12)^240-1))/((0.032/12)*(1+0.032/12)^240))
	Where A is the monthly payment.
	Therefore, A = 54000000*((0.032/12)*(1+0.032/12)^240))/((1+0.032/12)^240-1)) =	$        3,04,917.93
2)	Loan balance after 30 instalments is the PV of the balance 210 installments,
	which is 304917.93*((1+0.032/12)^210-1))/((0.032/12)*(1+0.032/12)^210))	$ 4,89,81,067.00
	Amount to paid in 210 months at 4.2% compounded monthly = 48981067*((0.042/12)*(1+0.042/12)^240))/((1+0.042/12)^240-1)) =	$        3,02,002.93