Question:
Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7696
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 = $7696 – $5200 = $2496
Thus, Simple Interest = $2496
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 × 2496/5200 × 8
= 249600/41600
= 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) = $5200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2496 (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 $5200
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = 416
Thus, simple Interest for 1 year = $416
Now,
∵ If the simple Interest is $416, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/416 years
∴ If the simple Interest is $2496, then the time = 1/416 × 2496 years
= 1 × 2496/416 years
= 2496/416 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(2) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(6) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(8) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?