Question

You just settled an insurance claim that calls for increasing payments over a 10-year period. The first payment will be paid one year from now in the amount of $5,000. The following payments will increase by 3.5 percent annually. What is the value of this settlement to you today if you can earn 6.5 percent on your investments? Multiple Choice a.$42,023.05 b.$36,408.28 d.$34,141.14 e.$41,422.89 f.$38,008.16 g.$38,008.16

Answer 1

Answer:

• Option e. $41,442.89

Explanation:

An annual payment over a 10-year period, with the first payment one year from now and 3.5 percent annual growth is modeled by the equation:

      $PV=\dfrac{C}{r-g}\times \big (1-\big(\dfrac{1+g}{1+r}\big)^n\big)$

Substitute with:

• C = $5,000
• r = 6.5% = 0.065
• g = 3.5% = 0.035
• n = 10

          $PV=\dfrac{\ 5,000}{0.065-0.035}\times \big (1-\big(\dfrac{1+0.035}{1+0.065}\big)^{10}\big)$

          $PV=\ 41,422.89\leftarrow answer$