Hello!
When I answered this problem, I used 4.08% for the semiannual withdrawals, and my answer turned out to be 2,573.07. However, the SOA solution used 4% instead and got 1430. Is there a standard number of decimals to use for the interest rate?
John made a deposit of 1000 into a fund at the beginning of each year for 20 years.
At the end of 20 years, he began making semiannual withdrawals of 3000 at the beginning of each six months, with a smaller final withdrawal to exhaust the fund. The fund earned an annual effective interest rate of 8.16%.
Calculate the amount of the final withdrawal.
SOA solution:
The accumulated value is 1000doubledot-s(20,0.816)= 50,382.16. This must provide a semi-annual annuitydue of 3000. Let n be the number of payments. Then solve 3000doubledot-a(n,0.04)=50,382.16 for n=26.47. Therefore, there will be 26 full payments plus one final, smaller, payment. The equation is 50,382.16=3000doubledot-a(26, 0.04) + X(1.04)^-26 with solution X = 1430. Note that the while the final payment is the 27th payment, because this is an annuity-due, it takes place 26 periods after the annuity begins.
I used the same way to solve the problem just with 4.08% instead of 4%
Thanks!!
When I answered this problem, I used 4.08% for the semiannual withdrawals, and my answer turned out to be 2,573.07. However, the SOA solution used 4% instead and got 1430. Is there a standard number of decimals to use for the interest rate?
John made a deposit of 1000 into a fund at the beginning of each year for 20 years.
At the end of 20 years, he began making semiannual withdrawals of 3000 at the beginning of each six months, with a smaller final withdrawal to exhaust the fund. The fund earned an annual effective interest rate of 8.16%.
Calculate the amount of the final withdrawal.
SOA solution:
The accumulated value is 1000doubledot-s(20,0.816)= 50,382.16. This must provide a semi-annual annuitydue of 3000. Let n be the number of payments. Then solve 3000doubledot-a(n,0.04)=50,382.16 for n=26.47. Therefore, there will be 26 full payments plus one final, smaller, payment. The equation is 50,382.16=3000doubledot-a(26, 0.04) + X(1.04)^-26 with solution X = 1430. Note that the while the final payment is the 27th payment, because this is an annuity-due, it takes place 26 periods after the annuity begins.
I used the same way to solve the problem just with 4.08% instead of 4%
Thanks!!
SOA #84