Question:
David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7488
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 = $7488 – $4800 = $2688
Thus, Simple Interest = $2688
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 × 2688/4800 × 7
= 268800/33600
= 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) = $4800
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2688 (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 $4800
= 7/100 × 4800
= 7 × 4800/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $2688, then the time = 1/336 × 2688 years
= 1 × 2688/336 years
= 2688/336 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(7) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.
(9) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.