Question:
Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11160
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 = $11160 – $6200 = $4960
Thus, Simple Interest = $4960
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 × 4960/6200 × 8
= 496000/49600
= 10 years (using formula)
Thus, Time (T) = 10 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) = $6200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4960 (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 $6200
= 8/100 × 6200
= 8 × 6200/100
= 49600/100 = 496
Thus, simple Interest for 1 year = $496
Now,
∵ If the simple Interest is $496, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/496 years
∴ If the simple Interest is $4960, then the time = 1/496 × 4960 years
= 1 × 4960/496 years
= 4960/496 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(3) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?
(6) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?