Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $8140

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 = $8140 – $5500 = $2640

Thus, Simple Interest = $2640

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 × 2640}/_{5500 × 8}

= ²⁶⁴⁰⁰⁰/₄₄₀₀₀

= 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) = $5500

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

Simple Interest = $2640 (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 $5500

= ⁸/₁₀₀ × 5500

= ^{8 × 5500}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $2640, then the time = ¹/₄₄₀ × 2640 years

= ^{1 × 2640}/₄₄₀ years

= ²⁶⁴⁰/₄₄₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(2) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.

(5) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.

(10) 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.