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) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(4) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(8) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?