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(Created page with "Happy and financially astute parents decide at the birth of their daughter that they will need to provide 50,000 at each of their daughter’s 18th , 19th , 20th and 21st birthdays to fund her college education. They plan to contribute <math>X</math> at each of their daughter’s 1 st through 17th birthdays to fund the four 50,000 withdrawals. They anticipate earning a constant 5% annual effective interest rate on their contributions. Let v = 1/1.05 Determine which of...") |
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Happy and financially astute parents decide at the birth of their daughter that they will need to provide 50,000 at each of their daughter’s 18th , 19th , 20th and 21st birthdays to fund her college education. They plan to contribute <math>X</math> at each of their daughter’s 1 st through 17th birthdays to fund the four 50,000 withdrawals. They anticipate earning a constant 5% annual effective interest rate on their contributions. | Happy and financially astute parents decide at the birth of their daughter that they will need to provide 50,000 at each of their daughter’s 18th , 19th , 20th and 21st birthdays to fund her college education. They plan to contribute <math display = "block">X</math> at each of their daughter’s 1 st through 17th birthdays to fund the four 50,000 withdrawals. They anticipate earning a constant 5% annual effective interest rate on their contributions. | ||
Let v = 1/1.05 | Let v = 1/1.05 | ||
Determine which of the following equations of value can be used to calculate <math>X</math>. | Determine which of the following equations of value can be used to calculate <math display = "block">X</math>. | ||
<ul class="mw-excansopts"> | <ul class="mw-excansopts"> | ||
<li><math>X\sum_{k=1}^{17}\nu^{k}=50,000[\nu+\nu^{2}+\nu^{3}+\nu^{4}]</math></li> | <li><math display = "block">X\sum_{k=1}^{17}\nu^{k}=50,000[\nu+\nu^{2}+\nu^{3}+\nu^{4}]</math></li> | ||
<li><math>X\sum_{k=1}^{16}1.05^{k}=50,000\left [1+\nu+\nu^{2}+\nu^{3}\right]</math></li> | <li><math display = "block">X\sum_{k=1}^{16}1.05^{k}=50,000\left [1+\nu+\nu^{2}+\nu^{3}\right]</math></li> | ||
<li><math>X\sum_{k=0}^{17}1.05^{k}=50,000\left [1+\nu+\nu^{2}+\nu^{3}\right]</math></li> | <li><math display = "block">X\sum_{k=0}^{17}1.05^{k}=50,000\left [1+\nu+\nu^{2}+\nu^{3}\right]</math></li> | ||
<li><math>X\sum_{k=1}^{17}1.05^{k}=50,000[1+\nu+\nu^{2}+\nu^{3}] | <li><math display = "block">X\sum_{k=1}^{17}1.05^{k}=50,000[1+\nu+\nu^{2}+\nu^{3}] | ||
</math></li> | </math></li> | ||
<li><math> X\sum_{k=0}^{17}\nu^{k}=50,000[\nu^{18}+\nu^{19}+\nu^{20}+\nu^{21}+\nu^{22}]</math></li> | <li><math display = "block"> X\sum_{k=0}^{17}\nu^{k}=50,000[\nu^{18}+\nu^{19}+\nu^{20}+\nu^{21}+\nu^{22}]</math></li> | ||
</ul> | </ul> | ||
{{soacopyright | 2023 }} | {{soacopyright | 2023 }} | ||
Revision as of 23:08, 18 November 2023
Happy and financially astute parents decide at the birth of their daughter that they will need to provide 50,000 at each of their daughter’s 18th , 19th , 20th and 21st birthdays to fund her college education. They plan to contribute
[[math]]X[[/math]]
at each of their daughter’s 1 st through 17th birthdays to fund the four 50,000 withdrawals. They anticipate earning a constant 5% annual effective interest rate on their contributions.
Let v = 1/1.05
Determine which of the following equations of value can be used to calculate
[[math]]X[[/math]]
.
- [[math]]X\sum_{k=1}^{17}\nu^{k}=50,000[\nu+\nu^{2}+\nu^{3}+\nu^{4}][[/math]]
- [[math]]X\sum_{k=1}^{16}1.05^{k}=50,000\left [1+\nu+\nu^{2}+\nu^{3}\right][[/math]]
- [[math]]X\sum_{k=0}^{17}1.05^{k}=50,000\left [1+\nu+\nu^{2}+\nu^{3}\right][[/math]]
- [[math]]X\sum_{k=1}^{17}1.05^{k}=50,000[1+\nu+\nu^{2}+\nu^{3}] [[/math]]
- [[math]] X\sum_{k=0}^{17}\nu^{k}=50,000[\nu^{18}+\nu^{19}+\nu^{20}+\nu^{21}+\nu^{22}][[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.