FM for Actuaries

182 CHAPTER 5
(a) What is the annual payment for Eddy?
(b) Find the net amount of the loan after 9 years.
5.54 A man is borrowing a housing loan of $180,000 from a bank for 10 years.
The quoted rate of interest is 8% per annum. Calculate the monthly installments
in arrears if the loan is based on (a) annual rest, and (b) monthly rest.
5.55 You borrow a loan of $100,000 to be repaid with quarterly installments in
15 years. The quoted rate of interest is 9% per annum based on annual rest.
Find the quarterly installments in arrears.
5.56 For a loan of $200,000 for 14 years to be repaid by monthly installments in
arrears, the quoted rate of interest is 8.7% per annum. Find the annualized
equivalent rate of interest on monthly rest if the loan is based on annual rest.
5.57 A loan of $10,000 is to be repaid in 10 years according to one of the following
arrangements:
(a) monthly payments in arrears with an APR of 8%,
(b) monthly payments in arrears with an APR of 9%, with a cash back of
$650 at the beginning (i.e., the loan amount is reduced by $650),
(c) monthly payments in arrears with a quoted interest rate of 7% on annual
rest.
Calculate the monthly payments for the three arrangements. Which arrangement
is more favorable to the borrower?
5.58 Calculate the annual effective rate for the three arrangements in Exercise
5.57.
5.59 A loan of $12,000 is to be repaid in 2 years according to one of the following
arrangements:
(a) repayment at the end of each month with APR of 12%,
(b) repayment of $1,650 at the beginning of each quarter.
Calculate the annual effective rate of interest for the two arrangements. Which
arrangement is more favorable to the borrower?
5.60 A 5-year automobile loan of amount $50,000 charges interest at a quoted flat
rate of interest of 6% per annum. The monthly installments are to be paid in
advance. Find the ENR and the effective rate of interest of the loan.