Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7238

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 = $7238 – $4700 = $2538

Thus, Simple Interest = $2538

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 × 2538}/_{4700 × 6}

= ²⁵³⁸⁰⁰/₂₈₂₀₀

= 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) = $4700

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2538 (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 = 6% of Principal

= 6% of $4700

= ⁶/₁₀₀ × 4700

= ^{6 × 4700}/₁₀₀

= ²⁸²⁰⁰/₁₀₀ = 282

Thus, simple Interest for 1 year = $282

Now,

∵ If the simple Interest is $282, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₂ years

∴ If the simple Interest is $2538, then the time = ¹/₂₈₂ × 2538 years

= ^{1 × 2538}/₂₈₂ years

= ²⁵³⁸/₂₈₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?

(4) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(8) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?

(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?