Question:
John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6556
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $6556 – $4400 = $2156
Thus, Simple Interest = $2156
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 2156/4400 × 7
= 215600/30800
= 7 years (using formula)
Thus, Time (T) = 7 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $4400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2156 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 7% of Principal
= 7% of $4400
= 7/100 × 4400
= 7 × 4400/100
= 30800/100 = 308
Thus, simple Interest for 1 year = $308
Now,
∵ If the simple Interest is $308, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/308 years
∴ If the simple Interest is $2156, then the time = 1/308 × 2156 years
= 1 × 2156/308 years
= 2156/308 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(4) If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.