Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $9088

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 = $9088 – $6400 = $2688

Thus, Simple Interest = $2688

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 × 2688}/_{6400 × 6}

= ²⁶⁸⁸⁰⁰/₃₈₄₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6400

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

Simple Interest = $2688 (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 $6400

= ⁶/₁₀₀ × 6400

= ^{6 × 6400}/₁₀₀

= ³⁸⁴⁰⁰/₁₀₀ = 384

Thus, simple Interest for 1 year = $384

Now,

∵ If the simple Interest is $384, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₄ years

∴ If the simple Interest is $2688, then the time = ¹/₃₈₄ × 2688 years

= ^{1 × 2688}/₃₈₄ years

= ²⁶⁸⁸/₃₈₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.

(3) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(4) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(8) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?