Question

Suppose you are 45 and have a $50,000 face amount, 15-year, limited-payment, participating policy (dividends will be used to build up the cash value of the policy). Your annual premium is $1,000. The cash value of the policy is expected to be $12,000 in 15 years. Using time value of money and assuming you could invest your money elsewhere for a 7 percent annual yield, calculate the net cost of insurance. Use Exhibit 1-B. (Do not round intermediate calculations. Round time value factor to 3 decimal places and final answer to the nearest whole number.)

Answer 1

13,129

Step-by-step explanation:

We will compare the end value of the policy with the future value of the premiums as moeny has a value over time of 7%

Future Value of the premiums at year 10th if they were invested elsewhere:

`C * (1-(1+r)^(-time) )/(rate) = FV\\`

C 1,000.00

time 15

rate 0.07

`1000 * (1-(1+0.07)^(-15) )/(0.07) = FV\\`

FV $25,129.0220

Salvage value of the policy if not exercise: 12,000

We "renounce" to 25,129 dollars for not investing the cash but we receive 12,000 therefore, the net value is the difference:

25,129 - 12,000 = 13,129

It cost 13,129 to get the insurance.

Answer 2

The Net cost of insurance $13,129.

Step-by-step explanation:

Annual premium (15 years) $15,000 ($1,000 × 15 years)

Time value of money

$1,000 × 25.129 = $25,129 (Exhibit 1-B, 15 years, 7%)

+$10,129 ($25,129 - 15,000)

Total cost of policy $25,129 ($15,000 + 10,129)

Cash value (end of 15 years) -$12,000

Net cost of insurance $13,129 ($25,129 - 12,000)

At a 7 percent annual yield, your account would have accumulated to $25,129 in 15 years. You have paid $13,129 for 15 years of insurance protection.