Business Mathematics
Simple and Compound Interest
Simple Interest Formulas
|
1 |
SI = |
Prt ÷ 100 |
|
2 |
A = |
P + SI |
|
3 |
r = |
(SI × 100) ÷ Pt |
|
4 |
t = |
(SI × 100) ÷ Pr |
|
5 |
P = |
(SI × 100) ÷ rt |
|
6 |
P = |
A − SI |
|
7 |
SI = |
A − P |
|
8 |
A = |
P [1 + (rt ÷ 100)] |
|
9 |
P = |
A ÷
[1 + (rt ÷ 100)] |
|
Where, |
|
|
SI = |
Simple Interest |
|
P = |
Principal |
|
r = |
Rate of interest per cent p.a. |
|
t = |
Time in years |
|
A = |
Amount (i.e. Principal + Interest) |
Compound
interest formulas
|
1 |
A = |
P (1 + i/x) ^n |
|
2 |
P = |
A ÷ (1 + i/x) ^n |
|
3 |
I = |
A – P |
|
4 |
I = |
P [{(1 + i/x) ^n} – 1] |
|
5 |
ERI = |
[(1 + i/x) ^x] – 1 |
|
Where, |
|
|
A = |
Amount (Principal + Total interest) = Future Value |
|
P = |
Principal = Present Value |
|
I = |
Total Interest Earned |
|
i = |
Interest of Rs 1 for one year |
|
i = |
r ÷ 100 |
|
r = |
Rate of interest per cent p.a. |
|
n = |
Total number of times interest is to be compounded |
|
x = |
Number of times interest is compounded per year |
|
ERI = |
Effective rate of interest |
Business Mathematics
Simple and Compound Interest
Selected Problems
Simple
Interest Problems
1. How much
interest will be earned on Rs 2,000 at 6 % simple interest for 2 years?
2. X deposited Rs 50,000 in a bank for two years with the interest rate of 5.5% p.a. How much interest would she earn and what would be the final value of the deposit?
3. Rahul deposited
Rs 1, 00,000 in his bank for 2 years at simple interest rate of 6%. How much
interest would he earn? How much would be the final value of deposit?
4. Find the rate of
interest if the amount owed after 6 months is Rs 1,050, borrowed amount being
Rs 1,000.
5. Rahul invested
Rs 70,000 in a bank at the rate of 6.5% p.a. Simple Interest. He received Rs 85,925
after the end of term. Find out the period for which sum was invested by Rahul.
6. Kapil deposited some amount in a bank for 7 ½ years at the rate of 6% p.a. simple interest. At the end of the term he received Rs 1, 01,500. Compute initial deposit of Kapil.
7. A sum of Rs 46,875 was lent out at simple interest and at the end of 1 year 8 months the total amount was Rs 50,000. Find the rate of interest per cent per annum.
8. What sum of
money will produce Rs 28,600 as an interest in 3 years and 3 months at 2.5% p.a.
simple interest?
9. In what time will Rs 85,000 amount to Rs 1, 57,675 at 4.5% p.a.?
10. If the amount
of Rs 500 in 3 years is Rs 575, what will be the amount of Rs 700 in 5 years?
11. A certain sum
of money becomes 3 times in 12 years by Simple Interest. What is the rate of
interest?
Compound Interest Problems
1. On what sum will
the compound interest at 5% per annum for two years compounded annually be Rs 1,640?
2. What annual rate
of interest compounded annually doubles an investment in 7 years.
Given that 2 ^(1/7) =
1.104090.
3. When will Rs
8,000 amount to Rs 8,820 at 10% per annum interest compounded half –yearly?
4. Find the rate
percent per annum if Rs 2, 00,000 amount to Rs 2, 31,525 in 1 ½ year interest being
compounded half – yearly.
5. A certain sum
invested at 4% per annum compounded semi- annually amounts to Rs 7830 at the end
of one year. Find the sum.
6. Rs 1600 invested
at 10% p.a. compounded semi- annually amounts to Rs 18,522. Find the time
period of the investment.
7. A person opened
an account on April, 2011 with a deposit of Rs 800. The account paid 6%
interest compounded quarterly. On October 1, 2011 he closed the account and
added enough additional money to invest in a 6-months time – deposit for Rs
1000. Earning 6% p.a. compounded monthly –
(a) How much additional
amount did the person invest on 1st October?
(b) What will be
the maturity value of his deposit on 1st April, 2012?
(c) How much total interest is earned?
Given that (1+i) ^n
is 1.03022500 for i = 1 ½%, n = 2 and (1+i) ^n is 1.03037751 for i = ½ % and n = 6.
8. Find the amount
of compound interest and effective rate of interest if an amount of Rs 20,000
is deposited in a bank for one year at the rate of 8% per annum compounded semi
annually.
9. Which is a
better investment 3% per year compounded monthly or 3.2% per year simple
interest?
Given that (1+
0.0025) ^12 = 1.0304.
10. In what time
will Rs 2000 lent at 5% p.a. fetch Rs 2050 at Compound Interest?
11. What sum at C.I
will amount to Rs 650 at the end of the year and to Rs 676 at the end of the second
year?
12. The interest on a sum for the first and second years is Rs 225 and Rs 238.50 respectively. Find the rate of interest and the sum?
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