Custom «Mathematics of Economics» Essay Paper

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

$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.

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.