Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9774

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 = $9774 – $5400 = $4374

Thus, Simple Interest = $4374

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 × 4374}/_{5400 × 9}

= ⁴³⁷⁴⁰⁰/₄₈₆₀₀

= 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) = $5400

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4374 (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 = 9% of Principal

= 9% of $5400

= ⁹/₁₀₀ × 5400

= ^{9 × 5400}/₁₀₀

= ⁴⁸⁶⁰⁰/₁₀₀ = 486

Thus, simple Interest for 1 year = $486

Now,

∵ If the simple Interest is $486, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₆ years

∴ If the simple Interest is $4374, then the time = ¹/₄₈₆ × 4374 years

= ^{1 × 4374}/₄₈₆ years

= ⁴³⁷⁴/₄₈₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(2) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(5) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.

(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?

(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?

(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(10) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.