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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