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Free «Mathematics of Economics» Essay Sample

2.2 (a) Interest (I) = Principal (P) x Rate (R) x Time (T)

For the $2,000 initial deposit to double, the amount required is $2,000, then P = $2,000, R = 8%, and I = $ 2,000.

$2,000 = $2,000 x 0.08 x T

T = 12.5 years (12 years and 6 months)

(b) Compound interest:  Total = Principal x (1 + Rate)years

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$4,000 = $2,000 x (1 + 0.07)years

$4,000 = $2,000(1.07)years

Years = 10. 25(10 years and 3 months)

2.3 Interest earned on $10,000 for 20 years at 7% simple interest is $14,000. Compound interest on $10,000 for 20 years at 7% will be $38,696.84. Therefore, amount earned under simple interest is less than amount earned in under compound interest by $ 24,696.84.

2.4 Interest earned on $1,000 for 5 years at 6% compound interest is $402.55. Interest earned on $1,000 for 5 years at 7% simple interest is $350. The best opinion is to invest the $1,000 for 5 years at 7% compound interest. 

2.5 Formula for payment amount per period

A = P [(1 +r)n/(1 + r)n – 1]

Where A is payment amount per period, P is loan amount, r is interest rate, and n is number of repayment periods.

Month/year

Amount paid

Principal paid

Interest paid

Balance

2013

1,285.46

829.11

416.35

5,121.84

2014

1,285.46

906.89

338.57

3,856.38

2015

1,285.46

991.97

253.49

2,570.92

2016

1,285,46

1,085.02

160.44

1,285.46

2017

1,285.46

1,186.81

58.65

0

2.9 Future value = Present value x (1 + Rate) years

Amount accumulated by:

(a) $7,000 in 8 years at 9% compounded annually is $13,947.94

(b) $1,250 in 12 years at 4% compounded annually is $2,001.29

2.17 If $1,00 is invested now, $1,500 two years from now, and $2,000 four years from now at an interest rate of 8% compounded annually, the total in 10 years will be $8,109.07

2. 19 Present value of; $3,000 two years from now at 9% compounded annually is $2,525.04, $4,000 occurring five years after (seven from now) at 9% compounded annually is $2,188.14, and $5,000 occurring seven years thereafter (12 years from now) at 9% compounded annually is $1,777.67. The total will be $6,490.85.

   

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