第14章复利–练习14.2 |套装1
问题11:Rakesh借出了Rs。 10000年,为期2年,每年20%,每年复利。如果半年加一次利息,他还能赚多少钱?
解决方案:
We have,
Principal (p) = Rs 10000
Rate (r) = 20% per annum
Time (t) = 2years
By using the formula,
A = P (1 + R/100)n
= 10000 (1 + 20/100)2
= 10000 (120/100)2 = Rs 14400
When the interest is compounded half-yearly,
New values are
Rate of interest becomes= 20/2% = 10%
Time = 2×2 years = 4years
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 10000 (1 + 10/100)4
= 10000 (110/100)4 = Rs 14641
∴ Rakesh could earn Rs (14641 – 14400) = Rs 241 more
问题12。罗默什借了一笔卢比。 245760,年利率12.5%,每年复利。在同一天,他以相同的利率将钱借给拉木,但每半年复利一次。 2年后找到他的收获。
解决方案:
Given:
Principal (p) = Rs 245760
Rate (r) = 12.5% per annum
Time (t) = 2years
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 245760 (1 + 12.5/100)2
= 245760 (112.5/100)2
= Rs 311040
Now, When compounded semi-annually,
Rate = 12.5/2% = 6.25%
Time = 2×2 years = 4years
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 245760 (1 + 6.25/100)4
= 245760 (106.25/100)4 = Rs 313203.75
∴ Romesh gain is Rs (313203.75 – 311040) = Rs 2163.75
问题13:找到David投资Rs会获得的金额。 8192,为期18个月,年利率为12½%,每半年复利一次。
解决方案:
Given,
Principal (p) = Rs 8192
Rate (r) = 12 ½ % per annum = 25/2×2 = 25/4% = 12.5/2% (half-yearly)
Time (t) = 18 months = 18/12 = 1 ½ years = (3/2) × 2 = 3years
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 8192 (1 + 12.5/2×100)3
= 8192 (212.5/200)3
= Rs 9826
∴ Amount is Rs 9826
问题14:找到Rs的复利。 15625,为期9个月,每年16%,每季度复利一次。
解决方案:
Given,
Principal (p) = Rs 15625
Rate (r) = 16% per annum = 16/4 = 4% (quarterly)
Time (t) = 9 months = 9/12 × 4 = 3quarters of a year
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 15625 (1 + 4/100)3
= 15625 (104/100)3
= Rs 17576
∴ CI = Rs 17576 – 15625 = Rs 1951
问题15. Rekha交纳卢比。一家外国银行中的16000,该银行每年按20%的利率每年复利一次支付利息,一年后找到Rekha收到的利息
解决方案:
Given is,
Principal (p) = Rs 16000
Rate (r) = 20% per annum = 20/4 = 5% (quarterly)
Time (t) = 1 year = 4 quarters of a year
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 16000 (1 + 5/100)4
= 16000 (105/100)4= Rs 19448.1
∴ CI = Rs 19448.1 – 16000 = Rs 3448.1
问题16。找到Rs的金额。每年以12500的年利率复合,第二年的年利率为15%,第二年的年利率为16%。
解决方案:
We have the following set of values,
Principal (p) = Rs 12500
Rate1 (r) = 15% and Rate2 = 16%
Time (t) = 2 years
By using the formula,
A = P (1 + R1/100 × 1 + R2/100) = 12500
Substituting the values we have,
(1 + 15/100 × 1 + 16/100) = 12500 (1.15 × 1.16)
= Rs 16675
∴ Amount after two years is Rs 16675
问题17. Ramu借了Rs。 15625从一家金融公司购买踏板车。如果利率是每年16%的复合年利率,那么他在2¼年后必须支付多少?
解决方案:
Given details are,
Principal (p) = Rs 15625
Rate (r) = 16%
Time (t) = 2 ¼ years
By using the formula,
A = P (1 + R/100 × 1 + R/100)= 15625
Substituting the values we have,
(1 + 16/100)2 × (1 + (16/4)/100)= 15625
(1 + 16/100)2 × (1 + 4/100)= 15625
(1.16)2 × (1.04)= Rs 21866
∴ Amount after 2 ¼ years is Rs 21866
问题18。如果每四个月计算一次利息,则125000的利率为6%?
解决方案:
Given,
Principal (p) = Rs 125000
Rate (r) = 6% per annum
Time (t) = 1 year
Since interest is compounded after 4months, interest will be counted as 6/3 = 2% and,
Time will be 12/4 = 3quarters
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 125000 (1 + 2/100)3
= 125000 (102/100)3
= Rs 132651
∴ Amount is Rs 132651
问题19:求出该本金的三年期复利,利率为5%,三年后年利率为5%,得出Rs。 12000年为单利。
解决方案:
Given,
Simple interest (SI) = Rs 12000
Rate (r) = 5% per annum
Time (t) = 3 years
SI = (PTR)/100P
= (SI×100)/(T×R)
Solving the equations,
= (12000×100) / (3×5)
= 1200000/15= 80000
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 80000 (1 + 5/100)3
= 80000 (105/100)3
= Rs 92610
∴ CI = Rs 92610 – 80000 = Rs 12610
问题20:一笔贷款以两年期每年20%的复合率贷出了两年。如果利息是每半年而不是每年支付一次,则利息为Rs。 482更多。求和。
解决方案:
We have,
Rate (r) = 20% per annum = 20/2 = 10% (half yearly)
Time (t) = 2 years = 2 × 2 = 4 half years
Principal be = Rs P
P (1 + R/100)n – P (1 + R/100)n
= 482P (1 + 10/100)4 – P (1 + 20/100)2
= 482P (110/100)4 – P (120/100)2
= 482P (1.4641) – P (1.44)
= 4820.0241P
= 482P = 482/0.0241
= 20000
∴ Amount is Rs 20000
问题21.以2%的年利率每年6½%的单利为Rs。 5200.在同一时期内,以相同的利率计算的总复利是多少?
解决方案:
Given is,
Rate = 6 ½ % per annum = 13/2%
Simple Interest (SI) = Rs 5200
Time (t) = 2 years
By using the formula,
SI = (PTR)/100P = (SI×100) / (T×R)
= (5200×100) / (2×13/2)
= (5200×100×2) / (2×13)
= 1040000/26
= Rs 40000
Now, P = Rs 40000R
= 13/2% = 6.5%T = 2years
By using the formula,
A = P (1 + R/100)n
Substituting the values we have,
= 40000 (1 + 6.5/100)2
= 40000 (106.5/100)2
= Rs 45369
∴ CI = Rs 45369 – 40000 = Rs 5369
问题22:该主体本金按3年年利率5%计算,在3年内按年利率5%计算Rs时,复利是多少? 1200为单利。
解决方案:
Rate = 5 % per annum
Simple Interest (SI) = Rs 1200
Time (t) = 3 years
By using the formula,
SI = (PTR)/100P = (SI×100) / (T×R)
= (1200×100) / (3×5)
= 120000/15
= Rs 8000
Now, P = Rs 8000R
= 5%T = 3years
By using the formula,
A = P (1 + R/100)n
= 8000 (1 + 5/100)3
= 8000 (105/100)3
= Rs 9261
∴ CI = Rs 9261 – 8000 = Rs 1261