(i) Bill and Hilary borrow $100,000 from a bank to purchase an apartment unit in

Question

(i) Bill and Hilary borrow $100,000 from a bank to purchase an apartment unit in Kingsford. The interest rate on the loan is fixed at 12% per annun compounded monthly. If the loan is be paid off by equal monthly payments over 25 years with (rounded to the nearest cent)? (ii) On the same day they borrow the $100,000 they deposit $10,000 into a newly opened bank account linked to their home loan. Interest carned on this account is added to the monthly payuent calculated in part (i), thus effectively increasing the monthly amount paid on the loan. The account carns interest at a rate of 3.6% per annum compounded monthly. If a balance of $10,000 is maintancd in the bank account until the loan is fully repaid, calculate how long it will take to pay off the loan. (Note: The last repayment will be less than the usual monthly ainount paidd.)

Explanation / Answer

(i) Total borrow amount, P = $100,000

Interest rate = 12% per annum = (12/12)% per month = 1% per month

Total payments = 25*12 months = 300 months

By the given conditions, 100000*(1+0.01)300 = A[1+(1+0.01)+(1+0.01)2+....+(1+0.01)299]

where A is the monthly payment.

i.e., 100000*(1.01)300 = A[1.01300-1]/(1.01-1)

i.e., A = 100000*(1.01)300*0.01/(1.01300-1)

i.e., A = 1053.22

Therefore, the monthly payment is $1053.22

ii) Deposited amount = $10,000

Interet rate = 3.6% per annum = 0.3% per month

Therefore, the interest earns from deposited amount is = $[10000(1+0.3/100)-10000] = $30

Now, the monthly payment = $(1053.22+30) = $1083.22

By the given condition, 100000*(1+0.01)n = (1083.22)[1+(1+0.01)+(1+0.01)2+....+(1+0.01)n-1]

i.e., 100000*(1.01)n = (1083.22)[1.01n-1]/(1.01-1)

i.e., 100000*0.01/1083.22 = (1.01n-1)/1.01n

i.e., 1-(1/1.01n) = 1000/1083.22

i.e., 1/1.01n = 1-1000/1083.22

i.e., 1/1.01n = 83.22/1083.22

i.e., 1.01n = 1083.22/83.22

i.e., n = 257.90

required payment = 21 years 6 months.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.