Theory of Interest
Annuities immediate, due, deferred, continuous, perpetuities
Determine the present value of regular payments of $250 to be made at the end of each of the next 50 years. The annual effective interest rate is 5%.
Find the present value of 50 regular annual payments of $3000 at the beginning of each year, starting now. The annual effective interest rate is 6%.
Find the present value at time 0 of regular payments of $50 at times 25 years, 26 years, and so on, with the last payment at time 40 years. Use an annual effective interest rate of 12%
4. $100 per year is received continuously from time 5 years to time 8 years. Assuming an annual effective interest rate of 4.5%, what is the accumulated value at time 10 years?
Payments of $5000 are received at the end of each year for 10 years, after which payments of $1000 are received at the end of each year forever. The annual effective interest rate is 9%. Determine the present value of these payments.
6. A perpetuity-immediate pays $X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian’s share of the present value of the original perpetuity is 40%, and Jeff’s share is K. Calculate K.
7. To accumulate $8000 at the end of 3n years, deposits of $98 are made at the end of each of the first n years and $196 at the end of each of the next 2n years. The annual effective interest rate is i. You are given . Determine i.
8. Connie buys an annuity-immediate from an insurance company. Connie pays $300,000 and in return...
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