5. Kevin wants to deposit some money in a bank. He surveys various banks and finds that Bank A promises to double his money in 6 years, Bank B promises to increase his money1- 1/2, times in 2-1/2 years and Bank C promises to treble his money in 8 years. Which bank is giving the highest rate of interest?
Answers
Solution :-
Let the money deposited by Kevin be
Rs. X
Bank A :-
Time = 6 years
Amount = Double the deposited money
= Rs. 2X
We know that
Interest = Amount - Principal
Interest = 2X - X = Rs. X
Let the rate of Interest be R% per annum
We know that
Simple Interest = PTR/100
=> X = (X×6×R)/100
=> X = 6XR/100
=> X = 3XR/50
=> 50X = 3XR
=> 50X/X = 3R
=> 50 = 3R
=> 3R = 50
=> R = 50/3 % or 16 2/3 % or 16.66%
Bank A gives 50/3 % or 16 2/3 % or 16.66% of rate of interest .
Bank B :-
Time = 2 1/2 years = 5/2 years
Amount = 1 1/2 times the deposited money
=> A = 1 1/2 × X
=> A = (3/2)×X
=> A = Rs. 3X/2
We know that
Interest = Amount - Principal
Interest = (3X/2) - X
=> Interest = (3X-2X)/2
=> Interest = Rs. X/2
Let the rate of Interest be R% per annum
We know that
Simple Interest = PTR/100
=> X/2 = (X×5×R)/(100×2)
=> X/2 = 5XR/200
=> X/2 = XR/40
=> 40X = 2XR
=> 40X/2X = R
=> 20 = R
=> R = 20%
=> 50 = 3R
Bank B gives 20% of rate of interest .
Bank C :-
Time = 8 years
Amount = Triple the deposited money
Amount = Rs. 3X
We know that
Interest = Amount - Principal
Interest = 3X-X = Rs. 2X
Let the rate of Interest be R% per annum
We know that
Simple Interest = PTR/100
=> 2X = (X×8×R)/100
=> 2X = 8XR/100
=> 2X = 2XR/25
=> 2X×25 = 2XR
=> 50X = 2XR
=> 50X/2X = R
=> 25 = R
=> R = 25%
Bank C gives 25% of rate of interest .
Now,
The rate of interest of Bank A = 16.66%
The rate of interest of Bank B = 20%
The rate of interest of Bank C = 25%
Answer :-
Bank C is giving highest rate of interest .
Used Formulae :-
• Simple Interest = PTR/100
• Amount = Principal + Interest
- P = Principal
- T = Time
- R = Rate of Interest