15. (10 points) A perpetuity with annual payment is payable at the end of 5 years from now. The first payment is 10 immediately at the end of 5 years. Each annual payment thereafter is increased by 10 until a payment of 50 is reached. Subsequent payments remain level at 50.
This perpetuity is purchased by means of 5 annual premiums, with the first premium of P due at the end of the first year. Each premium after the first is 110% of the preceding one. The annual effective rates are 5% during the first 5 years and 4% thereafter. Calculate P.
A. P < 169
B. 169 <P < 172
C. 172 < P < 175
D. 175 < P < 178