Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4500

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6390

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 = $6390 – $4500 = $1890

Thus, Simple Interest = $1890

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 × 1890}/_{4500 × 7}

= ¹⁸⁹⁰⁰⁰/₃₁₅₀₀

= 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) = $4500

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $1890 (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 = 7% of Principal

= 7% of $4500

= ⁷/₁₀₀ × 4500

= ^{7 × 4500}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = 315

Thus, simple Interest for 1 year = $315

Now,

∵ If the simple Interest is $315, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₅ years

∴ If the simple Interest is $1890, then the time = ¹/₃₁₅ × 1890 years

= ^{1 × 1890}/₃₁₅ years

= ¹⁸⁹⁰/₃₁₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

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

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(3) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(6) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

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

(8) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.

(9) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?