Li buys a $100 000 life insurance policy, which requires an annual premium of $420 or a monthly premium of $37. In either case, the premium is payable at the beginning of the period of coverage. What is the effective rate of interest Li pays, if he chooses monthly payment plan?

Question

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For the monthly payment plan, Li pays $37 per month or $444 annually. Therefore, he is effectively loaning the insurance company $444 and receiving $100,000 in return.

To calculate the effective interest rate, we need to find the annual percentage rate (APR) that would equate the $444 annual payment to a $100,000 present value.

Using the formula for present value of an annuity:
100,000 = 444 [1 - (1 + r/12)^-12*20]/(r/12)
Solving for r, we get r = 0.1304 or 13.04%.

Therefore, the effective rate of interest that Li pays for the monthly payment plan is 13.04%, which is the same as the APR. This is higher than the annual premium rate of $420, but Li may prefer the monthly payment plan for convenience or budgeting reasons.

Li Buys a $100 000 Life Insurance Policy, Which Requires