Simple Interest
MCQs Math


Question:     Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.


Correct Answer  9

Solution And Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $9632

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 = $9632 – $5600 = $4032

Thus, Simple Interest = $4032

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 × 4032/5600 × 8

= 403200/44800

= 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) = $5600

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

Simple Interest = $4032 (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 $5600

= 8/100 × 5600

= 8 × 5600/100

= 44800/100 = 448

Thus, simple Interest for 1 year = $448

Now,

∵ If the simple Interest is $448, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/448 years

∴ If the simple Interest is $4032, then the time = 1/448 × 4032 years

= 1 × 4032/448 years

= 4032/448 = 9 years

Thus, time (T) = 9 years Answer


Similar Questions

(1) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(3) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.

(7) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(10) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.


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