Question:
Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9916
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 = $9916 – $6700 = $3216
Thus, Simple Interest = $3216
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 × 3216/6700 × 8
= 321600/53600
= 6 years (using formula)
Thus, Time (T) = 6 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) = $6700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3216 (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 = 8% of Principal
= 8% of $6700
= 8/100 × 6700
= 8 × 6700/100
= 53600/100 = 536
Thus, simple Interest for 1 year = $536
Now,
∵ If the simple Interest is $536, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/536 years
∴ If the simple Interest is $3216, then the time = 1/536 × 3216 years
= 1 × 3216/536 years
= 3216/536 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(8) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?