Payments of 300, 500 and 700 are made at the end of years five, six and eight, respectively. Interest is accumulated at an annual effective rate of 4%. You are to find the point in time at which a single payment of 1,500 is equivalent to the above series of payments. You are given:
(i) X is the point in time calculated by the method of equated time.
(ii) Y is the exact point in time.
Calculate X + Y.
7. At time t = 0, Paul deposits P into a fund crediting interest at an effective annual interest rate of 8%. At the end of each year in years 6 through 20, Paul withdraws an amount sufficient to purchase an annuity-due of 100 per month for 10 years at a nominal interest rate of 12% compounded monthly. Immediately after the withdrawal at the end of year 20, the fund value is zero.
Calculate P.
8. A person age 40 wishes to accumulate a fund for retirement by depositing an amount X at the end of each year into an account paying 4% interest. At age 65, the person will use the entire account balance to purchase a 15-ear 5% annuity-immediate with annual payments of $10,000. Find X.
9. Eloise plans to accumulate 100,000 at the end of 42 years. She makes the following deposits:
(i) X at the beginning of years 1-14;
(ii) No deposits at the beginning of years 15-32, and
(iii) Y at the beginning of years 33-42.
The annual effective interest rate is 7% and X - Y = 100. Calculate Y.
10. You are given δ_t = 2 / (10+t), t ≥ 0.
Calculate a_{‾}4| .