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The proceeds of a 10,000 death benefit are left on deposit with an insurance company for seven years at an annual effective interest rate of 5 percent.The balance at the end of seven years is paid to the beneficiary in 120 equal monthly payments of X, with the first payment made immediately. During the payout period, interest is credited at an annual effective interest rate of 3 percent.Calculate X.

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Parrain

Answer: $135

Explanation:

First find the future value of the proceeds.

= 10,000 * (1 + 5%)⁷

= $14,071

The monthly payments are equal so X is an annuity and as the payment is made immediately, this is an Annuity due.

Convert the interest rate into monthly figure:

= 3%/12

= 0.25%

Present value of annuity = Annuity * (( 1 - (1 + r)^-n ) / r) * (1 + r)

14,071 = Annuity * ((1 - (1 + 0.25%) ⁻¹²⁰) / 0.25%) * (1 + 0.25%)

14,071 = Annuity * 103.82

Annuity = 14,071 / 103.82

= $135.53

= $135

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