Math Hacks: Shortcuts to Make Your Brain Calculate Faster Than a Calculator
1 . A
man deposits TK.1000 in a bank at 8% interest rate compounded annually. At
the end of the 3rd year, ehat will be the total amount including
interest ?
Solution
:
we know,
c= p.(1+r)^n
=1000×(1+0.08)^3=
1259.712
2. If
TK.1000 is invested in a account paying 10%
compounded annually, how much would be the
nearest
ending balance at the end of 3 years?
Solution:
C=p×(1+10/100)^3=1331.
3. A
person wishes to accumulate Tk. 500000 by the end of 15 years by making
equal half-yearly deposits over the next 15 years. If he earns 10% on
the investment, how much must he deposit at the end of each
half-year?
Solution
:
FV=A×{(1+i)^n-1}/i
>500000=A×{(1+0.05)^30-1}/.05
>A=500000/66.44
>A=7525.59
4. How
much interest will Tk. 10000 earns in 9 months at an annual rate of 6%.
Solution:
The
interest in 12 months is
tk. 10000
× 6/100
=tk. 600
So ,
interest in 1 month is tk. 600/12.=tk. 50
And
interest in 9 months is tk. 90×50 =tk. 450
5. What
annual rate was paid if Tk. 50000 earned
Tk. 3000
in interest in two years?
Solution:
Solution
: In 2 year tk. 50000 earned in tk. 3000
So In 1
year tk 100 earned in tk. 3000×100/
(5000×2)
=tk. 3.
6. A sum
of money at simple interest amounts to
Rs. 815
in 3 years and to Rs. 854 in 4 years. The
sum is:
Explanation:
S.I. for
1 year = Rs. (854 - 815) = Rs. 39.
S.I. for
3 years = Rs.(39 x 3) = Rs. 117.
Principal
= Rs. (815 - 117) = Rs. 698.
7. A man
took loan from a bank at the rate of 12% p.a. simple interest. After 3
years he had to pay Rs. 5400 interest only for the period.
The principal amount borrowed by him was:
Explanation:
Principal
= Rs. (100 x 5400 ) /12 x 3= Rs. 15000.
8. How
much time will it take for an amount of
Rs. 450
to yield Rs. 81 as interest at 4.5% per
annum of
simple interest?
Explanation:
Time = (100
x 81 years)/450 x 4.5 = 4 years.
9. A sum
of Rs. 12,500 amounts to Rs. 15,500 in
4 years
at the rate of simple interest. What is the rate of interest?
Explanation:
S.I. =
Rs. (15500 - 12500) = Rs. 3000.
Rate =
(100 x 3000 %)12500 x 4 = 6%
10. A
certain amount earns simple interest of Rs. 1750 after 7 years. Had the
interest been 2% more, how much more interest would it have earned?
Explanation:
We need
to know the S.I., principal and time to
find the
rate. Since the principal is not given, so data is inadequate.