Question

Kabayan plans to save as retirement savings. He went to the bank, where He was offered 2 options, as follows:

Option 1: Kabayan saves $ 1,000 at the end of every 4 months for 10 years. After 10 years, Kabayan no longer needs to save money, and only has to deposit his savings at the end of year 10 for the next 15 years

Option 2: kabayan does nothing for 10 years, then saves $ 6,000 at the end of each year for the next 15 years.

If the savings provide a compound interest of 6% per 4 months. Which option is more profitable for Kabayan?

Answer 1

Interest rate = 6% compounded every 4 months which is 2% (r1) every 4 months

Annual effective rate of Interest (r2) = [1 + (Interest rate compounded every 4 months / 3)]^³ = [1 + (6% / 3)]^³ = 1.0612 which is 6.12%

Option 1:

Saving every 4 month = 1,000 for 10 years which is 30 (n1) payment made

Future value of payment made after 10 years = 1,000 * {[(1 + r1)^ⁿ¹ - 1] / r1} = 1,000 * {[(1 + 0.02)^³⁰ - 1] / 0.02} = 40,568.08

This amount is further saved for 15 years at an annual effective rate of 6.12% whose future value would be 40,568.08 * (1 + 0.0612)^¹⁵ = 98,899.06

Option 2:

Future value of money saved for 15 (n2) years starting 10 yaers from now: 6,000 * {[(1 + r2)^ⁿ² - 1] / r2} = 6,000 * {[(1 + 0.0612)^¹⁵ - 1] / 0.0612} = 140,947.67

Option 2 is more profitable at the end of 25 years from now.