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 $9472 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $9472

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 = $9472 – $6400 = $3072

Thus, Simple Interest = $3072

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 × 3072}/_{6400 × 6}

= ³⁰⁷²⁰⁰/₃₈₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $3072 (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 $3072, then the time = ¹/₃₈₄ × 3072 years

= ^{1 × 3072}/₃₈₄ years

= ³⁰⁷²/₃₈₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.

(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?

(4) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(5) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?

(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?

(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(8) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(10) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?