Question:
Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7748
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 = $7748 – $5200 = $2548
Thus, Simple Interest = $2548
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 × 2548/5200 × 7
= 254800/36400
= 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) = $5200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2548 (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 $5200
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = 364
Thus, simple Interest for 1 year = $364
Now,
∵ If the simple Interest is $364, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/364 years
∴ If the simple Interest is $2548, then the time = 1/364 × 2548 years
= 1 × 2548/364 years
= 2548/364 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(4) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(10) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?