Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $10720

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 = $10720 – $6700 = $4020

Thus, Simple Interest = $4020

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 × 4020}/_{6700 × 6}

= ⁴⁰²⁰⁰⁰/₄₀₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6700

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

Simple Interest = $4020 (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 $6700

= ⁶/₁₀₀ × 6700

= ^{6 × 6700}/₁₀₀

= ⁴⁰²⁰⁰/₁₀₀ = 402

Thus, simple Interest for 1 year = $402

Now,

∵ If the simple Interest is $402, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₂ years

∴ If the simple Interest is $4020, then the time = ¹/₄₀₂ × 4020 years

= ^{1 × 4020}/₄₀₂ years

= ⁴⁰²⁰/₄₀₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(3) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.