# (Papers) ACET Paper May 2010 "CT1 – Financial Mathematics"

## (Papers) ACET Paper May 2010 "CT1 – Financial Mathematics"

**Q. 3) There are two types of annuities being offered by a
company with the following features :**

**Annuity 1**: A 10-year decreasing annuity, with annual
payments of 10, 9, 8, . . . ,1, the first payment being made at end of first
year.

**Annuity 2**: A yearly perpetuity, which pays 1 at end of year 1, 2 at end
of year 2, 3 at end of year 3, . . . , and 11 at end of year 11 . After year 11,
the payments remain constant at 11.

At an annual effective interest rate of i, the present value of Annuity 2 is twice the present value of Annuity 1. Calculate the value of Annuity 1.

**Q. 4)**

i) A loan of Rs. Y was taken for a period of n years at 7.75% p.a. convertible monthly. The loan was to be repaid through equated monthly installments (EMIs) of Rs.14612.884. The capital content of the 16th installment was Rs.3433.056.

(a) Find n and Y.

(b) Immediately after payment of 36 monthly installments, the borrower makes a
partrepayment of the loan by paying an amount of Rs.300,000/-. Hence, he gets a
rebate on interest rate and now is charged only 7.5% p.a. effective. Calculate
the revised EMI if the loan o/s is to be repaid over the remaining period.

ii) I have borrowed Rs. X for 10 years at an annual effective rate of 6.5% . If I pay the principal and accumulated interest in one lump sum at the end of 10 years, I would pay 486.091 more in interest than if I had repay the loan with 10 level payments at the end of each year. Calculate X.