Question

You purchase a life insurance policy which involves making 5 annual premium payments (the first payment starting today). The original premium is $1800 and the premium increases 4% each year. The time line for the payments is drawn for you.

Today 1 2 3 4
$1,800 $1,872 $1,947 $2,025 $2,106
Now assume the insurance company offers you a level payment plan that has the same present value as the payment stream above but where all the premiums are the same. If the insurance company earns 10% compounded annually on its assets, what would the level payments be?
Today 1 2 3 4
$X $X $X $X $X

Answer 1

$1,935.38

Step-by-step explanation:

Rate = 10% = 0.1

Present value of premiums = Premium Today + Premium 1/(1+r) + Premium 2/(1+r)^2 + Premium 3/(1+r)^3 + Premium 4/(1+r)^4

Present value of premiums = $1800 + $1872/1.1 + $1947/(1.1)^2 + $2025/(1.1)^3 + $2106/(1.1)^4

Present value of premiums = $1800 + $1701.82 + $1609.10 + $1521.41 + $1438.43

Present value of premiums = $8070.76

Present value of level payments = $8070.29 / (((1-(1+10%)^(-5))/10%)*(1+10%))

Present value of level payments = $8070.29 / 4.169865447

Present value of level payments = 1935.383791773462

Present value of level payments = $1,935.38