Question:
Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6956
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 = $6956 – $4700 = $2256
Thus, Simple Interest = $2256
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 × 2256/4700 × 6
= 225600/28200
= 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) = $4700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2256 (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 = 6% of Principal
= 6% of $4700
= 6/100 × 4700
= 6 × 4700/100
= 28200/100 = 282
Thus, simple Interest for 1 year = $282
Now,
∵ If the simple Interest is $282, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/282 years
∴ If the simple Interest is $2256, then the time = 1/282 × 2256 years
= 1 × 2256/282 years
= 2256/282 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(2) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(9) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.