Assume you win a $1,000,000 contest, and the prize will be paid in equal 10 equal installments over 10 years. The payments will be made on June 30 of each year beginning with June 30 this year. If the current rate of interest is 7 percent, what is the present value of your winnings? Use the information in the table to determine your answer.
Present value of an annuity of $1 at compound interest:
\(\begin{array}{ccccccc}
\text { Periods}&\mathbf{4 . 0 \%} & \mathbf{4 . 5 \%} & \mathbf{5 . 0 \%} & \mathbf{5 . 5 \%} & \mathbf{6 . 0 \%} & \mathbf{6 . 5 \%} & \mathbf{7 . 0 \%}&10.\%&11.0\%&12.0\%&13.0\% \
&0.961 & 0.956 & 0.952 & 0.947 & 0.943 & 0.938 & 0.934 & 0.909 & 0.900 & 0.892 & 0.884 \
1&54 & 94 & 38 & 87 & 40 & 97 & 58 & 09 & 90 & 86 & 96\&1.886 & 1.872 & 1.859 & 1.846 & 1.833 & 1.820 & 1.808 & 1.735 & 1.712 & 1.690 & 1.668 \
2&09 & 67 & 41 & 32 & 39 & 63 & 02 & 54 & 52 & 05 & 10\&2.775 & 2.748 & 2.723 & 2.697 & 2.673 & 2.648 & 2.624 & 2.486 & 2.443 & 2.401 & 2.361 \
3&09 & 96 & 25 & 93 & 01 & 48 & 32 & 85 & 71 & 83 & 15\&3.629 & 3.587 & 3.545 & 3.505 & 3.465 & 3.425 & 3.387 & 3.169 & 3.102 & 3.037 & 2.974 \
4&90 & 53 & 95 & 15 & 11 & 80 & 21 & 87 & 45 & 35 & 47\&4.451 & 4.389 & 4.329 & 4.270 & 4.212 & 4.155 & 4.100 & 3.790 & 3.695 & 3.604 & 3.517 \
5&82 & 98 & 48 & 28 & 36 & 68 & 20 & 79 & 90 & 78 & 23\&5.242 & 5.157 & 5.075 & 4.995 & 4.917 & 4.841 & 4.766 & 4.355 & 4.230 & 4.111 & 3.997 \
6&14 & 87 & 69 & 53 & 32 & 01 & 54 & 26 & 54 & 41 & 55\&6.002 & 5.892 & 5.786 & 5.682 & 5.582 & 5.484 & 5.389 & 4.868 & 4.712 & 4.563 & 4.422 \
7&05 & 70 & 37 & 97 & 38 & 52 & 29 & 42 & 20 & 76 & 61\&6.732 & 6.595 & 6.463 & 6.334 & 6.209 & 6.088 & 5.971 & 5.334 & 5.146 & 4.967 & 4.798 \
8&74 & 89 & 21 & 57 & 79 & 75 & 30 & 93 & 12 & 64 & 77\&7.435 & 7.268 & 7.107 & 6.952 & 6.801 & 6.656 & 6.515 & 5.759 & 5.537 & 5.328 & 5.131 \
9&33 & 79 & 82 & 20 & 69 & 10 & 23 & 02 & 05 & 25 & 66\&8.110 & 7.912 & 7.721 & 7.537 & 7.360 & 7.188 & 7.023 & 6.144 & 5.889 & 5.650 & 5.426 \
10&90 & 72 & 73 & 63 & 09 & 83 & 58 & 57 & 23 & 22 & 24
\end{array}\)
A) $253,785
B) $210,618
C) $173,256
D) $207,784

Question

Assume you win a $1,000,000 contest, and the prize will be paid in equal 10 equal installments over 10 years. The payments will be made on June 30 of each year beginning with June 30 this year. If the current rate of interest is 7 percent, what is the present value of your winnings? Use the information in the table to determine your answer.  
Present value of an annuity of $1 at compound interest:
  \(\begin{array}{ccccccc}
\text { Periods}&\mathbf{4 . 0 \%} & \mathbf{4 . 5 \%} & \mathbf{5 . 0 \%} & \mathbf{5 . 5 \%} & \mathbf{6 . 0 \%} & \mathbf{6 . 5 \%} & \mathbf{7 . 0 \%}&10.\%&11.0\%&12.0\%&13.0\% \
&0.961 & 0.956 & 0.952 & 0.947 & 0.943 & 0.938 & 0.934 & 0.909 & 0.900 & 0.892 & 0.884 \
1&54 & 94 & 38 & 87 & 40 & 97 & 58 & 09 & 90 & 86 & 96\&1.886 & 1.872 & 1.859 & 1.846 & 1.833 & 1.820 & 1.808 & 1.735 & 1.712 & 1.690 & 1.668 \
2&09 & 67 & 41 & 32 & 39 & 63 & 02 & 54 & 52 & 05 & 10\&2.775 & 2.748 & 2.723 & 2.697 & 2.673 & 2.648 & 2.624 & 2.486 & 2.443 & 2.401 & 2.361 \
3&09 & 96 & 25 & 93 & 01 & 48 & 32 & 85 & 71 & 83 & 15\&3.629 & 3.587 & 3.545 & 3.505 & 3.465 & 3.425 & 3.387 & 3.169 & 3.102 & 3.037 & 2.974 \
4&90 & 53 & 95 & 15 & 11 & 80 & 21 & 87 & 45 & 35 & 47\&4.451 & 4.389 & 4.329 & 4.270 & 4.212 & 4.155 & 4.100 & 3.790 & 3.695 & 3.604 & 3.517 \
5&82 & 98 & 48 & 28 & 36 & 68 & 20 & 79 & 90 & 78 & 23\&5.242 & 5.157 & 5.075 & 4.995 & 4.917 & 4.841 & 4.766 & 4.355 & 4.230 & 4.111 & 3.997 \
6&14 & 87 & 69 & 53 & 32 & 01 & 54 & 26 & 54 & 41 & 55\&6.002 & 5.892 & 5.786 & 5.682 & 5.582 & 5.484 & 5.389 & 4.868 & 4.712 & 4.563 & 4.422 \
7&05 & 70 & 37 & 97 & 38 & 52 & 29 & 42 & 20 & 76 & 61\&6.732 & 6.595 & 6.463 & 6.334 & 6.209 & 6.088 & 5.971 & 5.334 & 5.146 & 4.967 & 4.798 \
8&74 & 89 & 21 & 57 & 79 & 75 & 30 & 93 & 12 & 64 & 77\&7.435 & 7.268 & 7.107 & 6.952 & 6.801 & 6.656 & 6.515 & 5.759 & 5.537 & 5.328 & 5.131 \
9&33 & 79 & 82 & 20 & 69 & 10 & 23 & 02 & 05 & 25 & 66\&8.110 & 7.912 & 7.721 & 7.537 & 7.360 & 7.188 & 7.023 & 6.144 & 5.889 & 5.650 & 5.426 \
10&90 & 72 & 73 & 63 & 09 & 83 & 58 & 57 & 23 & 22 & 24
\end{array}\)  
A) $253,785
B) $210,618
C) $173,256
D) $207,784

Quizplus · Accepted Answer

The present value of the winnings can be calculated using the present value of an annuity formula, which requires the present value interest factor for annuities (PVIFA). For a 7% interest rate over 10 periods, the table shows a PVIFA of 7.023. Since the annual payment is $100,000 ($1,000,000 / 10), the present value is $100,000 * 7.023 = $702,300. However, the options provided do not match this calculation, suggesting a possible misunderstanding in the question's setup or a typographical error in the options. Based on the closest match principle and assuming each installment is $100,000, the correct calculation method leads to a value around $702,300, not directly matching any of the provided options.

Assume You Win a $1,000,000 Contest, and the Prize Will