Today, Malorie takes out a 10-year loan of $200,000, with a fixed interest rate of 3.7% per annum compounding monthly for the first 3 years. Afterwards, the loan will revert to the market interest rate.
Malorie will make monthly repayments over the next 10 years, the first of which is exactly one month from today. The bank calculates her current monthly repayments assuming the fixed interest rate of 3.7% will stay the same over the coming 10 years.
(d) After the fixed interest period, the market interest rate becomes 4.7% per annum effective. Assuming the interest rate stays at this new level for the remainder of the term of the loan, calculate the new monthly installment.
Formula to calculate monthly payment | |||
Monthly payment | Present value/(1-((1+r)^-n)/r) | ||
No of payments (n) | 120 | 10*12 | |
Monthly interest rate (r) | 0.31% | 3.7%/12 | |
Monthly payment | 200,000/(1-(1.0031^-120)/0.0031)) | ||
Monthly payment | 200,000/100.174819 | ||
Monthly payment | $1,996.51 | ||
b. | |||
Calculate value of loan after three years | |||
Value of loan | Monthly payment*(1-(1+r^-n)/r) | ||
Value of loan | 1996.51*(1-(1.0037^-84)/0.0037) | ||
Value of loan | 1996.51*73.9035779 | ||
Value of loan | $147,549.23 | ||
Calculation of revised monthly payment | |||
No of payments (n) | 84 | 7*12 | |
Monthly interest rate (r) | 0.39% | 4.7%/12 | |
Monthly payment | 147549.23/(1-(1.0039^-84)/0.0039)) | ||
Monthly payment | 147549.23/71.46239 | ||
Monthly payment | $2,064.71 | ||
Thus, the new monthly instalment would be $2,064.71 | |||
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