Max and Tyler both make deposits of $30,000. Max’s bank credits his deposit with a simple interest rate of 10% annually. Tyler’s bank credits him with an annual compounded interest rate of 6%. At time t the forces of interest are equal.

Determine which person’s bank account has more money and by how much.

• Max: $5,532.52
• Tyler: $7.44
• Max: $5,946.14
• Tyler: $16,444.87
• Insufficient information to solve

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

Solution: C

Max: deposit = 30,000 simple interest = 10%

Tyler: deposit = 30,000 compound interst = 6%

Max’s force of interest: [math] .1/(1 +.1t) [/math]

Tyler’s force of interest: 30,000(1 + .1(7.153)) = 51,459

Set equal: [math] .0583 = .1/(1 +.1t), \, t = 7.153 [/math]

Accumulated value of Max’s deposit: 30,000(1 + .1(7.153)) = 51,459

Accumulated value of Tyler’s deposit: 30,000(1 + .06)^7.153 = 45,512.86

Max – Tyler = 5,946.14

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