Question:
Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10540
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 = $10540 – $6200 = $4340
Thus, Simple Interest = $4340
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 × 4340/6200 × 7
= 434000/43400
= 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) = $6200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4340 (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 $6200
= 7/100 × 6200
= 7 × 6200/100
= 43400/100 = 434
Thus, simple Interest for 1 year = $434
Now,
∵ If the simple Interest is $434, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/434 years
∴ If the simple Interest is $4340, then the time = 1/434 × 4340 years
= 1 × 4340/434 years
= 4340/434 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(6) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.