Question:
John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6248
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 = $6248 – $4400 = $1848
Thus, Simple Interest = $1848
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 × 1848/4400 × 6
= 184800/26400
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1848 (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 $4400
= 6/100 × 4400
= 6 × 4400/100
= 26400/100 = 264
Thus, simple Interest for 1 year = $264
Now,
∵ If the simple Interest is $264, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/264 years
∴ If the simple Interest is $1848, then the time = 1/264 × 1848 years
= 1 × 1848/264 years
= 1848/264 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(6) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.