Question:
Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8528
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 = $8528 – $5200 = $3328
Thus, Simple Interest = $3328
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 × 3328/5200 × 8
= 332800/41600
= 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) = $5200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3328 (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 $3328, then the time = 1/416 × 3328 years
= 1 × 3328/416 years
= 3328/416 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(8) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.