Simple Interest
Math MCQs

Question :    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.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $11316

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 = $11316 – $6900 = $4416

Thus, Simple Interest = $4416

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 × 4416}/_{6900 × 8}

= ⁴⁴¹⁶⁰⁰/₅₅₂₀₀

= 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) = $6900

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

Simple Interest = $4416 (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 $6900

= ⁸/₁₀₀ × 6900

= ^{8 × 6900}/₁₀₀

= ⁵⁵²⁰⁰/₁₀₀ = 552

Thus, simple Interest for 1 year = $552

Now,

∵ If the simple Interest is $552, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₂ years

∴ If the simple Interest is $4416, then the time = ¹/₅₅₂ × 4416 years

= ^{1 × 4416}/₅₅₂ years

= ⁴⁴¹⁶/₅₅₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(3) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(5) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?

(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.