Stat 274 Theory of Interest Practice Problem Set 4 Brian ...

[Pages:17]Stat 274 Theory of Interest

Practice Problem Set 4

Brian Hartman Brigham Young University

SOA #173

An insurer enters into a four-year contract today. The contract requires the insured to deposit 500 into a fund that earns an annual effective rate of 5.0%, and from which all claims will be paid. The insurer expects that 100 in claims will be paid at the end of each year, for the next four years. At the end of the fourth year, after all claims are paid, the insurer is required to return 75% of the remaining fund balance to the insured. To issue this policy, the insurer incurs 100 in expenses today. It also collects a fee of 125 at the end of two years. Calculate the insurer's yield rate. [9%, 24%, 39%, 54%, 69%]

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SOA #105

A bank agrees to lend 10,000 now and X three years from now in exchange for a single

repayment of 75,000 at the end of 10 years. The bank charges interest at an annual

effective

rate

of

6%

for

the

first

5

years

and

at

a

force

of

interest

t

=

1 t +1

for

t

5.

Calculate X .

[23,500; 24,000; 24,500; 25,000; 25,500]

3

SOA #137

Jennifer establishes an investment account to pay for college expenses for her daughter. She plans to invest X at the beginning of each month for the next 21 years. Beginning at the end of the 18th year, she will withdraw 20,000 annually. The final withdrawal at the end of the 21st year will exhaust the account. She anticipates earning an annual effective yield of 8% on the investment. Calculate X . [137.90, 142.80, 146.40, 150.60, 154.30]

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SOA #141

An investor decides to purchase a five-year annuity with an annual nominal interest rate of 12% convertible monthly for a price of X . Under the terms of the annuity, the investor is to receive 2 at the end of the first month. The payments increase by 2 each month thereafter. Calculate X . [2015, 2386, 2475, 2500, 2524]

5

SOA #145

A perpetuity-due with annual payments consists of ten level payments of X followed by a series of increasing payments. Beginning with the eleventh payment, each payment is 1.5% larger than the preceding payment. Using an annual effective interest rate of 5%, the present value of the perpetuity is 45,000. Calculate X . [1679, 1696, 1737, 1763, 1781]

6

SOA #109

On January 1, 2003 Mike took out a 30-year mortgage loan in the amount of 200,000 at an annual nominal interest rate of 6% compounded monthly. The loan was to be repaid by level end-of-month payments with the first payment on January 31, 2003. Mike repaid an extra 10,000 in addition to the regular monthly payment on each December 31 in the years 2003 through 2007. Determine the date on which Mike will make his last payment (which is a drop payment). [July 31, 2013; November 30, 2020; December 31, 2020; December 31, 2021; January 31, 2022]

7

SOA #150

A loan of 20,000 is repaid by a payment of X at the end of each year for 10 years. The loan has an annual effective interest rate of 11% for the first five years and 12% thereafter. Calculate X . [2739.5, 3078.5, 3427.5, 3467.5, 3484.5]

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