Calculate the amount and compound interest on
(a) Rs 10800 for 3 years at per annum compounded annually.
(b) Rs 18000 for years at 10% per annum compounded annually.
(c) Rs 62500 for years at 8% per annum compounded half yearly.
(d) Rs 8000 for 1 year at 9% per annum compound half yearly.
(You could use the year by year calculation using SI formula to verify)
(e) Rs 10000 for 1 year at 8% per annum compounded half yearly.
Answers
Answer:
Compound Interest Formulas and Calculations:
Calculate Accrued Amount (Principal + Interest) A = P(1 + r/n)nt
Calculate Principal Amount, solve for P. P = A / (1 + r/n)nt
Calculate rate of interest in decimal, solve for r. r = n[(A/P)1/nt - 1]
Calculate rate of interest in percent. R = r * 100.
Calculate time, solve for t.
Step-by-step explanation:
Question 1: Calculate the amount and compound interest on
(a) Rs 10,800 for 3 years at 12.5% per annum compounded annually.
Answer:
A
=
P
(
1
+
R
100
)
t
P = 10800, R
=
12
1
2
%
and t = 3 years
So,
A
=
10800
(
1
+
25
200
)
3
=
10800
(
1
+
1
8
)
3
=
10800
(
9
8
)
3
=
10800
×
9
8
×
9
8
×
9
8
=
15377.34
So, Interest
=
A
–
P
=
15377.54
−
10800
=
4577.34
(b) Rs 18,000 for 2.5 years at 10% per annum compounded annually.
Answer: Amount
=
18000
(
1
+
10
100
)
2
=
18000
×
11
10
×
11
10
=
21780
Interest after 2 years
=
21780
−
18000
=
3780
Interest after half year
=
21780
×
10
100
×
1
2
=
1089
Total interest after 2.5 years
=
3780
+
1089
=
4869
(c) Rs 62,500 for 1.5 years at 8% per annum compounded half yearly.
Answer: Amount after 1.5 year
=
62500
(
1
+
4
100
)
3
Rate has been halved because interest is compounded half yearly, time has been doubled for the same reason.
=
62500
×
26
25
×
26
25
×
26
25
=
70304
So, interest
=
70304
−
62500
=
7804
(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly.
Answer:
A
=
8000
(
1
+
9
200
)
2
=
8000
×
209
200
×
209
200
=
8736.20
So, interest
=
8736.20
−
8000
=
736.20
(e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.
Answer:
A
=
10000
(
1
+
4
100
)
2
=
10000
×
26
25
×
26
25
=
10816
So, interest
=
10816
−
10000
=
816
Alternate method: Calculating big multiplication can be tedious. Compound interest can also be calculated by finding yearly amount for each year separately.
1st half year
10000
+
400
=
10400
2nd half year
10400
+
416
=
10816