Question:
Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11050
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 = $11050 – $6500 = $4550
Thus, Simple Interest = $4550
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 × 4550/6500 × 10
= 455000/65000
= 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) = $6500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4550 (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 = 10% of Principal
= 10% of $6500
= 10/100 × 6500
= 10 × 6500/100
= 65000/100 = 650
Thus, simple Interest for 1 year = $650
Now,
∵ If the simple Interest is $650, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/650 years
∴ If the simple Interest is $4550, then the time = 1/650 × 4550 years
= 1 × 4550/650 years
= 4550/650 = 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 3% simple interest.
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(4) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(6) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?