Compound interest is the interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from previous periods.
Amount (A) = P(1 + R/100)^{t}
Interest = Amount - Principal
Here P = principal, R = rate of interest and t = time of investment
Problem 1 :
a) What will an investment of $3000 at 10% p.a. Compound interest amount to after 3 years?
b) What part of this is interest?
Solution :
P= $3000, R = 10% ==> 0.10 and T = 3 years
a) Amount A = P(1 + R/100)^{t}
= 3000(1 + 0.1)^{3}
= 3000(1.1)^{3}
= 3000(1.331)
= $3993
b) Compound interest = Amount – Principal
= 3993 – 3000
= $993
So, interest is $993.
Problem 2 :
How much compound interest is earned by investing $20,000 for 4 years at 12% p.a.?
Solution :
P= $20000, R = 12% and T = 4 years
Amount A = P(1 + R/100)^{t}
= 20000(1 + 0.12)^{4}
= 20000(1.12)^{4}
= 20000(1.57351936)
= 31470.39
Compound interest = Amount – Principal
= 31470.39 – 20000
= 11470.39
So, compound interest is $11470.39.
Problem 3 :
$5000 is invested for 2 years at 10% p.a. What will this investment amount to if the interest is calculated as :
a) Simple interest
b) Compound interest?
Solution :
P= $5000, R = 10% ==> 0.10 and T = 2 year
a) Simple interest I = (P × T × R)/100
= (5000 × 2 × 10)/100
= 100000/100
= 1000
So, simple interest is $1000.
Total amount = P + I
= 5000 + 1000
= 6000
So, total amount is £6000.
b) Compound interest = P(1 + R/100)^{t}
= 5000(1 +
0.1)^{2}
= 5000(1.1)^{2}
= 5000(1.21)
= $6050
So, compound interest is $6050.
Problem 4 :
a) What will an investment of $30,000 at 10% p.a. Compound interest amount to after 4 years?
b) What part of this is interest?
Solution :
P= $30000, R = 10% and T = 4 years
a) Amount A = P(1 + R/100)^{t}
= 30000(1 + 0.1)^{4}
= 30000(1.1)^{4}
= 30000(1.4641)
= $43923
b) Compound interest = Amount – Principal
= 43923 – 30000
= $13923
So, interest is $13923.
Problem 5 :
How much compound interest is earned by investing €80,000 at 9% p.a. over a 3 year period?
Solution :
Principal amount P= $80000
Rate R = 9%
Time T= 3 years
Amount A = P(1 + R/100)^{t}
= 80000(1 + 0.09)^{3}
= 80000(1.09)^{3}
= 80000(1.295029)
= 103602.32
Compound interest = Amount – Principal
= 103602.32 – 80000
= 23602.32
So, compound interest is $23602.32.
Problem 6 :
$6000 is invested for 2 years at 15% p.a. What will this investment amount to if the interest is calculated as :
a) Simple interest
b) Compound interest?
Solution :
P= $6000, R = 15% ==> 0.15 and T = 2 years
a) Simple interest = (P × T × R)/100
= 6000 × 2 × 0.15
= 1800
So, simple interest is $1800.
Total amount = P + I
= 1800 + 6000
= 7800
So, total amount is $7800.
b) Compound interest = P(1 + R/100)^{t}
= 6000(1 + 0.15)^{2}
= 6000(1.15)^{2}
= 6000(1.3225)
= 7935
So, compound interest is $7935.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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