Question

Consider the following annuities: Annuity A requires payments of $150 per month for ten years, and at the end of ten years has a total balance of $21,000. Annuity B requires annual payments of $1,000 for twelve years and has a total balance of $16,000 at the end of the 12 year term. Annuity C requires monthly payments of $100 for thirty years, and at the end of the thirty-year term has a total balance of $41,000. Which annuity paid out the most interest over its respective term?

Answer 1

Annuity C

Step-by-step explanation:

With annuity A, we deposit 10⋅12⋅$150, which means D10=$18,000. Since A(10)=$21,000, I10=$21,000−$18,000=$3,000.

With annuity B, we deposit 12⋅$1,000, which means D12=$12,000. Since A(12)=$16,000, I12=$16,000−$12,000=$4,000.

Finally, with annuity C, we deposit 30⋅12⋅$100, which means D30=$36,000. Since A(30)=$41,000, I30=$41,000−$36,000=$5,000. We conclude annuity C paid the most interest.

Answer 2

C paid out he most nominal interest: 6,000

B is the annuity which give a better return as it generate on average 500 interest per year.

Step-by-step explanation:

For the total interest we will calcualte the total contribution and subtract it from the total balance ofthe annuity

A:

150 per month x 12 month x 10 year = 18,000

21,000 - 18,000 = 3,000 interest

3,000 / 10 = 300 interest per year

B:

1,000 per year x 12 year = 12,000

16,000 - 12,000 = 4,000 interest

4,000 / 12 = 500 interest per year

C: 100 x 12 months x 30 years = 36,000

41,000 - 36,000 = 5,000

5,000 / 30 = 166,66 per year