Question

A four-year annuity of eight $5,000 semiannual payments will begin nine years from now, with the first payment coming 9.5 years from now. (Do not round intermediate calculations. Round the final answers to 2 decimal places. Omit $ sign in your response.)

If the discount rate is 6 percent compounded monthly, what is the value of this annuity five years from now? Value of the annuity $

If the discount rate is 6 percent compounded monthly, what is the value three years from now? Value of the annuity $

If the discount rate is 6 percent compounded monthly, what is the current value of the annuity? Value of the annuity $

Can you use BA PLUS Calculator for solution

Answer 1

Knowledge required:

Presnt value of an amount A for r % of discount rate for n years = A/(1+r)ⁿ

Solution:

Step 1: Computation of value of annuity at beginning of year 10/ end of year 9

= 5000(1.005)⁶ +5000(1.005)¹² +5000(1.005)¹⁸ +5000(1.005)²⁴ +5000(1.005)³⁰ +5000(1.005)³⁶ +5000(1.005)⁴² +5000(1.005)⁴⁸

= $ 35042 approx

Step 2: Value of annuity at the end of year 5/beginning of year 6

= Value at end of year 9/( 1.005)^4*12 = 35042/(1.005)⁴⁸

= $ 27582 ( Answer 1)

Step 3: Value of annuity at the end of year 3/beginning of year 4

= Value at end of year 9/( 1.005)^6*12 = 35042/(1.005)⁷²

= $ 24470 ( Answer 2)

Step 3: Current value of annuity /beginning of year 1

= Value at end of year 9/( 1.005)^9*12 = 35042/(1.005)¹⁰⁸

= $ 20448 ( Answer 3)