Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8200

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 = $8200 – $5000 = $3200

Thus, Simple Interest = $3200

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 × 3200}/_{5000 × 8}

= ³²⁰⁰⁰⁰/₄₀₀₀₀

= 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) = $5000

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3200 (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 $5000

= ⁸/₁₀₀ × 5000

= ^{8 × 5000}/₁₀₀

= ⁴⁰⁰⁰⁰/₁₀₀ = 400

Thus, simple Interest for 1 year = $400

Now,

∵ If the simple Interest is $400, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₀ years

∴ If the simple Interest is $3200, then the time = ¹/₄₀₀ × 3200 years

= ^{1 × 3200}/₄₀₀ years

= ³²⁰⁰/₄₀₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?

(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.

(5) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(7) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.

(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.