FM for Actuaries

Loans and Costs of Borrowing 175
remaining obligation in 12 equal annual payments at 6%, the first payment
being made 1 year after the 3rd defaulted payment. Calculate the amount of
the principal repaid in the 6th rescheduled payment.
5.18 Warren purchased a $100,000 house 5 years ago. The mortgage was to be
repaid with monthly payments in arrears over 15 years. The nominal rate
of interest is 8% compounded monthly. In order to shorten the term of the
mortgage by 5 years so as to reduce interest, Warren negotiates with the
lender so that the remaining outstanding loan balance is to be repaid in 5
years by larger monthly level payments. How much interest can Warren
save?
5.19 Tim borrowed $10,000 at effective rate of 10% for 16 years and the loan
was scheduled to be repaid with level annual installment payments at the
end of each year until maturity. During the 6th year, the market interest rate
dropped and Tim negotiated with the lender so that the interest rate charged
in subsequent years after the 6th payment would be 8% and the term of the
loan would be unchanged. Calculate
(a) the level annual installment payments after the 6th payment,
(b) the interest loss to the lender as a result of the negotiation.
5.20 Lily borrowed a loan to study in a university. Now that she has graduated, she
needs to repay the loan with quarterly installments for 6 years. The first payment
(due after 3 months) and the second payment (due after 6 months) are
both $400, and the payment increases by $30 every half-year, until it reaches
$610 and becomes level. The nominal interest rate is 8% compounded quarterly.
Find the amount of principal repaid in the 9th payment.
5.21 Sally deposited $200 into a fund which earns 5% per year. The interest can
only be reinvested at 4% per annum.
(a) Find the accumulated value of the investment after 5 years.
(b) Find the effective annual rate of interest of the investment.
5.22 Philip invests $500 at the beginning of each month into an account earning
an effective rate of 6% for 2 years. The interest earned from the account can
only be reinvested at an effective rate of 5%.
(a) Find the accumulated value of the investment after 3 years.
(b) Compare your answer with the case when all interests are reinvested at
6% effective.