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) 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.

(2) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.