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 $9112 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $9112

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 = $9112 – $6700 = $2412

Thus, Simple Interest = $2412

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 × 2412}/_{6700 × 6}

= ²⁴¹²⁰⁰/₄₀₂₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $2412 (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 $2412, then the time = ¹/₄₀₂ × 2412 years

= ^{1 × 2412}/₄₀₂ years

= ²⁴¹²/₄₀₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.

(3) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?

(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(10) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.