Question 4 12 CT1 September 2008 An individual takes out a 25-year bank loan of 300,000 to purchase a house. The individual agrees to pay only the interest payments, monthly in arrear, for the first 15 years where- upon he repays half of the capital as a lump sum. He then pays only the interest for the remaining 10 years, quarterly in arrear, and repays the other half of the capital as a lump sum at the end of the term. (i) Calculate the total amount of interest paid by the individual, assuming an effective rate of interest of 82% p.a. [5] The individual believes that he can earn a nominal rate of interest convertible half-yearly of 9% p.a. from a separate savings account. (ii) Calculate the level contribution he must make monthly in advance to the savings account in order to repay half the capital after 15 years. [4] (iii) The individual made the monthly contributions calculated in (ii) to the savings account. However, over the first 15 years, the effective rate of return earned on the savings account was 10% per annum. The individual used the proceeds at that time to repay as much of the loan as possible and then decided to repay the remainder of the loan by level instalments of interest and capital. After the first 15 years, the effective rate of interest changed to 7% per annum. Calculate the level payment he must make, payable monthly in arrear, to repay the loan over the final 10 years of the loan. [5] [Total 14] Question 4 12 CT1 September 2008 An individual takes out a 25-year bank loan of 300,000 to purchase a house. The individual agrees to pay only the interest payments, monthly in arrear, for the first 15 years where- upon he repays half of the capital as a lump sum. He then pays only the interest for the remaining 10 years, quarterly in arrear, and repays the other half of the capital as a lump sum at the end of the term. (i) Calculate the total amount of interest paid by the individual, assuming an effective rate of interest of 82% p.a. [5] The individual believes that he can earn a nominal rate of interest convertible half-yearly of 9% p.a. from a separate savings account. (ii) Calculate the level contribution he must make monthly in advance to the savings account in order to repay half the capital after 15 years. [4] (iii) The individual made the monthly contributions calculated in (ii) to the savings account. However, over the first 15 years, the effective rate of return earned on the savings account was 10% per annum. The individual used the proceeds at that time to repay as much of the loan as possible and then decided to repay the remainder of the loan by level instalments of interest and capital. After the first 15 years, the effective rate of interest changed to 7% per annum. Calculate the level payment he must make, payable monthly in arrear, to repay the loan over the final 10 years of the loan. [5] [Total 14]
