Question

Mr. Gomez has spent 8 months saving $ 1000 at the beginning of each fortnight, the interest rate being equal to 10% capitalizable biweekly. The day he will make the seventeenth deposit, Mr. Gomez finds out that the interest rate goes up to from that moment on to 11.5% capitalizable every fortnight and decides to increase the biweekly savings to $ 1300 as of that moment. Calculate the amount and interest earned after two years

Answer 1

Given information:

Total period = 2 years = 52 * 2 = 104 weeks = 52 biweekly payments

Number of payments of $1,000 = 16

Number of payments of $1,300 = 52 - 16 = 36

Total amount paid = $1,000 * 16 + $1,300 * 36 = $16,000 + $46,800 = $62,800

Interest rate up to 16 biweekly periods = 10% capitalized biweekly

Interest after to 16 biweekly periods = 11.5% capitalized biweekly

Future value of 16 biweekly payments of $1,000 at the end of 2 years

= $1,000 * Future Value of Annuity Due of $1 at 10% capitalized biweekly for 16 periods

    * Future Value of $1 at 11.5% capitalized biweekly for 36 periods

= $1,000 * [((1+0.10/26)^16 – 1)/(0.10/26)*(1+0.10/26)] * (1+0.115/26)^36

= $1,000 * 16.53327287 * 1.17219688

= $19,380.25

Future value of 36 biweekly payments of $1,300 at the end of 2 years

= $1,300 * Future Value of Annuity Due of $1 at 11.5% capitalized biweekly for 36 periods

= $1,300 * [((1+0.115/26)^36 – 1)/(0.115/26)*(1+0.115/26)]

= $1,300 * 39.10366429

= $50,834.76

Total Value of Investment at the end of 2 years = $19,380.25 + $50,834.76 = $70,215.01

Of which Interest = $70,215.01 - $62,800 = $7,415.01.