Question

PRESENT VALUE OF AN ANNUITY

Find the present values of these ordinary annuities. Discounting occurs once a year. Round your answers to the nearest cent.

$600 per year for 10 years at 6%.

$  

$300 per year for 5 years at 3%.

$  

$800 per year for 10 years at 0%.

$  

Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.

$600 per year for 10 years at 6%.

$  

$300 per year for 5 years at 3%.

$  

$800 per year for 10 years at 0%.

$  

Answer 1

Present Value :

$600 per year for 10 years at 6%

= $ 600 * 1/(1.06)^ 1 + $ 600 * 1/(1.06)^2 + $ 600 * 1/(1.06)^3+...+ $ 600 * 1/(1.06)^10

= $ 4,416.05

$300 per year for 5 years at 3%

= $ 300 * 1/(1.03) ^ 1+ $ 300 * 1/(1.03) ^ 2 + $ 300 * 1/(1.03) ^ 3 + $ 300 * 1/(1.03) ^ 4 +$ 300 * 1/(1.03) ^ 5

= $ 1,373.91

$800 per year for 10 years at 0%.

= $ 800 * 1/(1) ^ 1+ $ 800 * 1/(1) ^ 2 + $ 800 * 1/(1) ^ 3 + ...+ $ 800 * 1/(1) ^ 10

= $ 8,000

Annuities Due :

$600 per year for 10 years at 6%.:

= Present Value * ( 1+ Rate of Interes/100)

= $ 4,416.05* (1.06)

= $ 4,681.01

$300 per year for 5 years at 3%.

= Present Value * ( 1+ Rate of Interes/100)

= $ 1,373.91 * (1.03)

= $ 1,415.13

$800 per year for 10 years at 0%.

= Present Value * ( 1+ Rate of Interes/100)

=$ 8,000 * (1+0/100)

= $ 8,000