Simple Interest
MCQs Math


Question:     Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution And Explanation

Solution

Given,

Principal (P) = $7000

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10360

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual 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 = $10360 – $7000 = $3360

Thus, Simple Interest = $3360

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 × 3360/7000 × 8

= 336000/56000

= 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) = $7000

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3360 (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 $7000

= 8/100 × 7000

= 8 × 7000/100

= 56000/100 = 560

Thus, simple Interest for 1 year = $560

Now,

∵ If the simple Interest is $560, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/560 years

∴ If the simple Interest is $3360, then the time = 1/560 × 3360 years

= 1 × 3360/560 years

= 3360/560 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?

(2) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?

(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(5) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

(8) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.


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