Question

Assume you are to receive a 10-year annuity with annual payments of $1000. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 10. You will invest each payment in an account that pays 9 percent compounded annually. Although the annuity payments stop at the end of year 10, you will not withdraw any money from the account until 25 years from today, and the account will continue to earn 9% for the entire 25-year period. What will be the value in your account at the end of Year 25 (rounded to the nearest dollar)? Select one: a. $48,000 b. $35,967 c. $48,359 d. $55,340 Clear my choice Question 4

Answer 1

Answer:

d. $55,340

Explanation:

You begin to receive the annuity at the end of the year 1, so its begin to capitalize on year 2 because the first year  

there is no money to capitalize.  

The second year begin to apply over the first annuity the interest payment,the next ten 10 years from 2 to 11 the deposits start to capitalize compounded anually at 9% of interest.  

Compound interest, means that each time that the account generate interests, this total amount apply to the next period as basis to calculate the next interests, not only grows the interest payment over the initial capital if not over the past interest generated.  

At the end of the 25 years you will have $55,340 in the account available.    

$ 1,000 $ 1,090  2   Year  

$ 1,000 $ 2,278  3   Year  

$ 1,000 $ 3,573  4   Year  

$ 1,000 $ 4,985  5   Year  

$ 1,000 $ 6,523  6   Year  

$ 1,000 $ 8,200  7   Year  

$ 1,000 $ 10,028  8   Year  

$ 1,000 $ 12,021  9   Year  

$ 1,000 $ 14,193  10   Year  

$ 1,000 $ 16,560  11   Year  

        $ 18,051  12   Year  

        $ 19,675  13   Year  

        $ 21,446  14   Year  

        $ 23,376  15   Year  

        $ 25,480 16   Year  

        $ 27,773  17   Year  

        $ 30,273  18   Year  

        $ 32,997  19   Year  

        $ 35,967  20   Year  

        $ 39,204  21   Year  

        $ 42,733  22   Year  

        $ 46,579  23   Year  

        $ 50,771  24   Year  

        $ 55,340 25   Year