Question:
Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9230
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 = $9230 – $6500 = $2730
Thus, Simple Interest = $2730
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 × 2730/6500 × 7
= 273000/45500
= 6 years (using formula)
Thus, Time (T) = 6 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) = $6500
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2730 (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 $6500
= 7/100 × 6500
= 7 × 6500/100
= 45500/100 = 455
Thus, simple Interest for 1 year = $455
Now,
∵ If the simple Interest is $455, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/455 years
∴ If the simple Interest is $2730, then the time = 1/455 × 2730 years
= 1 × 2730/455 years
= 2730/455 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(6) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
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