Question:
Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $12420
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 = $12420 – $6900 = $5520
Thus, Simple Interest = $5520
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 × 5520/6900 × 8
= 552000/55200
= 10 years (using formula)
Thus, Time (T) = 10 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) = 8% per annum
Simple Interest = $5520 (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 $6900
= 8/100 × 6900
= 8 × 6900/100
= 55200/100 = 552
Thus, simple Interest for 1 year = $552
Now,
∵ If the simple Interest is $552, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/552 years
∴ If the simple Interest is $5520, then the time = 1/552 × 5520 years
= 1 × 5520/552 years
= 5520/552 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.