Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $7020

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 = $7020 – $4500 = $2520

Thus, Simple Interest = $2520

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 × 2520}/_{4500 × 8}

= ²⁵²⁰⁰⁰/₃₆₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4500

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

Simple Interest = $2520 (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 $4500

= ⁸/₁₀₀ × 4500

= ^{8 × 4500}/₁₀₀

= ³⁶⁰⁰⁰/₁₀₀ = 360

Thus, simple Interest for 1 year = $360

Now,

∵ If the simple Interest is $360, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₀ years

∴ If the simple Interest is $2520, then the time = ¹/₃₆₀ × 2520 years

= ^{1 × 2520}/₃₆₀ years

= ²⁵²⁰/₃₆₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?

(2) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.

(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?

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

(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

(10) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.