Question:
Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10212
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 = $10212 – $6900 = $3312
Thus, Simple Interest = $3312
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 × 3312/6900 × 6
= 331200/41400
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3312 (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 = 6% of Principal
= 6% of $6900
= 6/100 × 6900
= 6 × 6900/100
= 41400/100 = 414
Thus, simple Interest for 1 year = $414
Now,
∵ If the simple Interest is $414, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/414 years
∴ If the simple Interest is $3312, then the time = 1/414 × 3312 years
= 1 × 3312/414 years
= 3312/414 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(4) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(6) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(10) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?