Question

Find the future values of these ordinary annuities. Compounding occurs once a year. Round your answers to the nearest cent. $200 per year for 10 years at 12%. $ 621.17 $100 per year for 5 years at 6%. $ $1,000 per year for 2 years at 0%. $ Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent. $200 per year for 10 years at 12%. $ $100 per year for 5 years at 6%. $ $1,000 per year for 2 years at 0%. $

Answer 1

Answer:

Normal:

$ 3,509.7470

$    563.7093

$ 2,000.00

Due:    

 $3,930.9167

 $   597.5319

 $ 2,000.00

Explanation:

We solve using the formula for common annuity and annuity-due on each case:

$C \times \frac{(1+r)^{time} }{rate} = FV$

$C \times \frac{(1+r)^{time} }{rate}(1+rate) = FV$ (annuity-due)

First:

C 200.00

time 10

rate 0.12

$200 \times \frac{11+0.12)^{10} }{0.12} = FV$

$200 \times \frac{11+0.12)^{10} }{0.12}(1+0.12) = FV$

Normal:  $3,509.7470

Due:       $3,930.9167

Second:

$100 \times \frac{(1+0.06)^{5} }{0.06} = FV$

$100 \times \frac{(1+0.06)^{5} }{0.06} (1+0.06)= FV$

$563.7093

$597.5319

Third:

No interest so no time value of money the future value is the same as the sum of the receipts regardless of time or being paid at the beginning or ending.

1,000  + 1,000 = 2,000