Gaston has an annuity that pays $250 at the beginning of each quarter. If the economy grows at a rate of 4.97% annually, what is the value of the annuity if he received it in a lump sum now rather than over a period of eight years?

$1,617.76
$1,698.17
$6,471.06
$6,792.67

Question

Gaston has an annuity that pays $250 at the beginning of each quarter. If the economy grows at a rate of 4.97% annually, what is the value of the annuity if he received it in a lump sum now rather than over a period of eight years?

 $1,617.76
 $1,698.17
 $6,471.06
 $6,792.67

tkhunny · Answer

Convert your interest to Quarterly.
Create an appropriate quarterly discount factor.
You're almost done.

mrs.irwin · Answer

how am I supposed to come up with the quarterly discount factor?

mrs.irwin · Answer

@tkhunny

anonymous · Answer

It's $6,792.67 @Mrs.Irwin

mrs.irwin · Answer

@Hannah_Waller are you 100% sure. I cannot fail?

anonymous · Answer

haha yes @Mrs.Irwin

mrs.irwin · Answer

@Hannah_Waller thank you so much!!!

anonymous · Answer

@misty1212 can u finish helping me on my problem?

tkhunny · Answer

i = 4.97% annually = 0.0497
j = i/4 = 0.012425 = Quarterly interest
v = 1/(1+j) = 0.987727486 = Quarterly Discount Factor

It's just a definition.

Your payments now look like this, discounted to the beginning:..

250 + 250v + 250v^2 + 250v^3 + ....

Make sense?