Question 36 • Mathematics for Data and Financial Literacy
Grace, a 50 -year-old teacher, purchases a whole life insurance policy with a $150,000 death benefit. The policy includes a cash value component that grows at a fixed interest rate of 3.6% annually. Grace contributes $4,000 annually to the policy's cash value portion, and the accumulated cash value will continue to grow at the same 3.6% interest rate. What will the cash value portion be after 10 years? Use the formula cap A is equal to the fraction with numerator cap p times open paren open paren 1 plus r over n close paren raised to the n t power minus 1 close paren and denominator open paren r over n close paren
Answer
A
40 dollars comma 000 point 0 0
B
90 dollars comma 468 point 8 5
C
47 dollars comma 143 point 0 2
D
56 dollars comma 971 point 4 9
Explanation
Use the given formula with annual contributions of $4,000, an annual interest rate of 0.036, one compounding period per year, and 10 years: A = 4,000 × ((1.036)^10 − 1) ÷ 0.036. This gives approximately $47,143.02, so the cash value is choice C, $47,143.02.
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