Calculate the amount and compound interest on,
(a) $18,000 for 2*1/2 years at 10% per annum compounded annually.
(b) $62,500 for 1*1/2 years at 8% per annum compounded half yearly.
(c) $8,000 for 1 year at 9% per annum compounded half yearly.
(You could use the year by year calculation using S.I. formula to verify).
(d) 10,000 for 1 year at 8% per annum compounded half yearly.
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Answers
time=2*1/2yrs➡1yr
rate%=10%
hence,c.i for 1 yr =$18000*1*10/100
=$1800
amount=p+I
➡$18,000+$1800=$19800
b) compounding half yearly,
r=8% =4%per half yr
t=1*1/2yr=n=3half yrs.
hence,a=p(1+r/100)n(here,n is the power)
➡$62500(1+4/100)3
=$62500(25/26)3
=$62500*26/25*26/25*26/25
=$4*26*26*26
=$70304
hence, amount=$70304
c.i=a-p
➡$70304-62500
=$7804
c)compounded half yearly,
r=9%p.a=4.5%per half year
t=1yr
hence,amount=p(1+r/100)n(here n is considered as power)
➡$8000(1+4.5/100)1
=$8,000.045
c.i=a-p
➡$8000.045-8000
=$0.045
d) compounded half yearly,
r=8%p.a=4%per half yr
t=1yr
hence, amount=p(1+r/100)n{here,n is considered as power}
➡$10,000(1+4/100)1
=$10,000.04
c.i=a-p
➡$10,000.04-$10,000
=$0.04
a) principle=$18,000
time=2*1/2yrs➡1yr
rate%=10%
hence,c.i for 1 yr =$18000*1*10/100
=$1800
amount=p+I
➡$18,000+$1800=$19800
b) compounding half yearly,
r=8% =4%per half yr
t=1*1/2yr=n=3half yrs.
hence,a=p(1+r/100)n(here,n is the power)
➡$62500(1+4/100)3
=$62500(25/26)3
=$62500*26/25*26/25*26/25
=$4*26*26*26
=$70304
hence, amount=$70304
c.i=a-p
➡$70304-62500
=$7804
c)compounded half yearly,
r=9%p.a=4.5%per half year
t=1yr
hence,amount=p(1+r/100)n(here n is considered as power)
➡$8000(1+4.5/100)1
=$8,000.045
c.i=a-p
➡$8000.045-8000
=$0.045
d) compounded half yearly,
r=8%p.a=4%per half yr
t=1yr
hence, amount=p(1+r/100)n{here,n is considered as power}
➡$10,000(1+4/100)1
=$10,000.04
c.i=a-p
➡$10,000.04-$10,000
=$0.04
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