Question

Two annuities have equal present values. The first is an annuity-immediate with quarterly payments of $X for 10 years. The second is an increasing annuity-immediate with 10 annual payments, where the first payment is $500 and subsequent payments increase by 10% per year. Find X if the annual effective interest rate is 5%. (Answer: 188.28)

Answer 1

To find X, calculate the present values of both annuities and equate them using the appropriate formulas for each. X is approximately 188.28

Step-by-step explanation:

To find the value of X, we need to calculate the present values of both annuities and equate them. The present value of the first annuity with quarterly payments of X for 10 years can be calculated using the formula:

Present Value = X × ((1 + r/q) nq - 1) / (r/q)

where r is the annual interest rate, q is the number of payments per year, and n is the number of years. The present value of the second annuity can be calculated by finding the present value of each individual payment and adding them up using the formula:

Present Value = payment1 / (1 + r) + payment2 / (1 + r)2 + ... + paymentn / (1 + r)n

Plugging in the given values and equations, we can solve for X and find that X is approximately 188.28