Question:
Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11524
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 = $11524 – $6700 = $4824
Thus, Simple Interest = $4824
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 × 4824/6700 × 8
= 482400/53600
= 9 years (using formula)
Thus, Time (T) = 9 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) = $6700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4824 (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 $6700
= 8/100 × 6700
= 8 × 6700/100
= 53600/100 = 536
Thus, simple Interest for 1 year = $536
Now,
∵ If the simple Interest is $536, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/536 years
∴ If the simple Interest is $4824, then the time = 1/536 × 4824 years
= 1 × 4824/536 years
= 4824/536 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(4) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(8) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(9) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?