Eric deposits $6,000 into an account that gives 6% interest annually. He takes out $2,000 at the end of years 7, 14, and 21 at a penalty of 4%. What is the accumulated value of the deposit at the end of year 23?

• $16,678.50
• $5,507.16
• $11,783.36
• $8,695.22
• $35,053.63

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Solution: C

Initial deposit: 6,000

Withdrawals: 2,000 at the end of 7, 14, 21

Interest rate = .06

penalty = .04

Accumulated value = 6,000(1.06)²³ – 2,000(1.04)(1.06)¹⁶ - 2,000(1.04)(1.06)⁹ - 2,000(1.04)(1.06)² =$11,783.36

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.