Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 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) = 8% per annum

Amount (A) = $9984

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 = $9984 – $6400 = $3584

Thus, Simple Interest = $3584

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 × 3584}/_{6400 × 8}

= ³⁵⁸⁴⁰⁰/₅₁₂₀₀

= 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) = 8% per annum

Simple Interest = $3584 (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 = 8% of Principal

= 8% of $6400

= ⁸/₁₀₀ × 6400

= ^{8 × 6400}/₁₀₀

= ⁵¹²⁰⁰/₁₀₀ = 512

Thus, simple Interest for 1 year = $512

Now,

∵ If the simple Interest is $512, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₂ years

∴ If the simple Interest is $3584, then the time = ¹/₅₁₂ × 3584 years

= ^{1 × 3584}/₅₁₂ years

= ³⁵⁸⁴/₅₁₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(5) Sarah took a loan of $5700 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.

(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(8) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(9) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.