I can apply the strategy to problem solving questions

(apply everyday compounding rates)

Debt Race

On 1st June 2008 five people A, B, C, D and E each borrow $100,000.

Each year, starting 1st June 2009, each is charged interest on the amount owed at the start of the previous year, which is added to the balance. Each year, each will pay off a lump sum of their debt, which is taken from the balance.

The rates and amounts for each borrower is as follows:

A

B

C

D

E

3%

6%

9%

12%

15%

$12,000

$14,000

$16,000

$18,000

$20,000

The question is this: Which borrower will be the first to pay off his debt

C with 9.51 years

A =  9.73 years.

100,000 x 1.03 = 103000 - 12000 = 91000 x 1.03 = 93730 - 12000 = 81730 x 1.03 = 84181.9 - 12000 = 72181.9 x 1.03 = 74347.357 - 12000 = 62347.357 x 1.03 = 64217.77771 - 12000 = 52217.77771 x 1.03 = 53784.3110413 - 12000 = 41784.3110413 x 1.03 = 43037.8403725 - 12000 = 31037.8403725 x 1.03 = 31968.9755837 - 12000 = 19968.9755837 x 1.03 = 20568.0448512 - 12000 = 8568.04485123 x 1.03 = 8825.08619676 ÷ 12000 = 0.73 + 9 = 9.73

B = 9.60 years.

100,000 x 1.06 = 106000 - 14000 = 92000 x 1.06 = 97520 - 14000 = 83520 x 1.06 = 88531.2 - 14000 = 74531.2 x 1.06 = 79003.072 - 14000 = 65003.072 x 1.06 = 68903.25632 - 14000 = 54903.25632 x 1.06 = 58197.4516992 - 14000 = 44197.4516992 x 1.06 = 46849.2988012 - 14000 = 32849.2988012 x 1.06 = 34820.2567292 - 14000 = 20820.2567292 x 1.06 = 22069.472133 - 14000 = 8069.47213297 x 1.06 =  8553.64046095 ÷ 14000 = 0.60 + 9 = 9.60

C = 9.59 years.

100,000 x 1.09 = 109000 - 16000 = 93000 x 1.09 = 101370 - 16000 = 85370 x 1.09 = 93053.3 - 16000 = 77053.3 x 1.09 = 83988.097 - 16000 = 67988.097 x 1.09 = 74107.02573 - 16000 = 58107.02573 x 1.09 = 63336.6580457 - 16000 = 47336.6580457 x 1.09 = 51596.9572698 - 16000 = 35596.9572698 x 1.09 = 38800.6834241 - 16000 = 22800.6834241 x 1.09 = 24852.7449323 - 16000 = 8852.74493226 x 1.09 = 9649.49197617 ÷ 16000 = 0.59 + 9 = 9.59

D = 9.69 years.

100,000 x 1.12 = 112000 - 18000 = 94000 x 1.12 = 105280 - 18000 = 87280 x 1.12 = 97753.6 - 18000 = 79753.6 x 1.12 = 89324.032 - 18000 = 71324.032 x 1.12 = 79882.91584 - 18000 = 61882.91584 x 1.12 = 69308.8657408 - 18000 = 51308.8657408 x 1.12 = 57465.9296297 - 18000 = 39465.9296297 x 1.12 = 44201.8411853 - 18000 = 26201.8411853 x 1.12 = 29346.0621275 - 18000 = 11346.0621275 x 1.12 = 12707.5895828 ÷ 18000 = 0.69 + 9 = 9.69

E = 9.92 years.

100,000 x 1.15 = 115000 - 20000 = 95000 x 1.15 = 109250 - 20000 = 89250 x 1.15 = 102637.5 - 20000 = 82637.5 x 1.15 = 95033.125 - 20000 = 75033.125 x 1.15 = 86288.09375 - 20000 = 66288.09375 x 1.15 = 76231.3078125 - 20000 = 56231.3078125 x 1.15 = 64666.0039844 - 20000 = 44666.0039844 x 1.15 = 51365.904582 - 20000 = 31365.904582 x 1.15 = 36070.7902693 - 20000 = 16070.7902693 x 1.15 = 18481.4088097 ÷ 20000 = 0.91 + 9 = 9.92