Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $11180

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 = $11180 – $6500 = $4680

Thus, Simple Interest = $4680

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 × 4680}/_{6500 × 8}

= ⁴⁶⁸⁰⁰⁰/₅₂₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $6500

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

Simple Interest = $4680 (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 $6500

= ⁸/₁₀₀ × 6500

= ^{8 × 6500}/₁₀₀

= ⁵²⁰⁰⁰/₁₀₀ = 520

Thus, simple Interest for 1 year = $520

Now,

∵ If the simple Interest is $520, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₀ years

∴ If the simple Interest is $4680, then the time = ¹/₅₂₀ × 4680 years

= ^{1 × 4680}/₅₂₀ years

= ⁴⁶⁸⁰/₅₂₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(2) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

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

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(6) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.

(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.