Question

(2 points) Juan purchases an annuity for 4980 dollars that will make 18 annual payments, the first to come in one year. If the effective rate of interest is 8.6 percent, how much is each annual payment? Answer dollars.

Answer 1

Initial Value of Annuity = $ 4980, Number of Payments = 18 implying annuity tenure of 18 years as each payment comes in at the end of each year, Effective Interest Rate = 8.6 %

As per the principles of time value of money, the total present value of the 18 annuities should equal the annuity's purchase value so as to be fairly priced and avoid arbitrage.

Let the annual annuity value be $ K

therefore, 4980 = K x (1/0.086) x [1-{1/(1.086)^(18)}]

4980 = 8.994217 x K

K = $ 553.69

NOTE: Please raise separate qeuries for solutions to the remaining unrelated questions as one query is restricted to the solution of only one question (with upto four sub-parts).