Question

As a settlement for an insurance​ claim, Craig was offered one of two choices. He could either accept a​ lump-sum amount of

​$10,802

​now, or accept

monthly

payments of

​$121

for the next

ten

years. If the money is placed into a trust fund earning

6.67​%

compounded

annually

which is the better option and by how​ much?

The

▼

lump sum

monthly payments

option is better by

​$nothing.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

Option 1:

Lump Sum = $10,802

Option 2:

Monthly Payment = $121
Time Period = 10 years or 120 months

Annual Interest Rate = 6.67%

Monthly Interest Rate = (1 + Annual Interest Rate)^(1/12) - 1
Monthly Interest Rate = (1 + 0.0667)^(1/12) - 1
Monthly Interest Rate = 1.005395 - 1
Monthly Interest Rate = 0.005395 or 0.5395%

Present Value = $121/1.005395 + $121/1.005395^2 + … + $121/1.005395^119 + $121/1.005395^120
Present Value = $121 * (1 - (1/1.005395)^120) / 0.005395
Present Value = $121 * 88.171189
Present Value = $10,668.71

The lump sum option is better by $133.29 ($10,802.00 - $10,668.71).