Question:
Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9880
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 = $9880 – $5200 = $4680
Thus, Simple Interest = $4680
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 × 4680/5200 × 10
= 468000/52000
= 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) = $5200
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4680 (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 $5200
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = 520
Thus, simple Interest for 1 year = $520
Now,
∵ If the simple Interest is $520, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/520 years
∴ If the simple Interest is $4680, then the time = 1/520 × 4680 years
= 1 × 4680/520 years
= 4680/520 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?
(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(7) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?