Question:
Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10595
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 = $10595 – $6500 = $4095
Thus, Simple Interest = $4095
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 × 4095/6500 × 7
= 409500/45500
= 9 years (using formula)
Thus, Time (T) = 9 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) = $6500
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4095 (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 $6500
= 7/100 × 6500
= 7 × 6500/100
= 45500/100 = 455
Thus, simple Interest for 1 year = $455
Now,
∵ If the simple Interest is $455, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/455 years
∴ If the simple Interest is $4095, then the time = 1/455 × 4095 years
= 1 × 4095/455 years
= 4095/455 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(3) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(8) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?