Simple Interest
Math MCQs

Question :    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.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4752

Rate of Simple Interest (R) = 2%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$4752 = P (1 + 2% × 4)

⇒ $4752 = P (1 + ²/₁₀₀ × 4)

⇒ $4752 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4752 = P (1 + ⁸/₁₀₀)

⇒ $4752 = P (^{100 + 8}/₁₀₀)

⇒ $4752 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4752

⇒ P = ⁴⁷⁵²/_¹⁰⁸/100

⇒ P = 4752 × ¹⁰⁰/₁₀₈

⇒ P = ^{4752 × 100}/₁₀₈

⇒ P = ⁴⁷⁵²⁰⁰/₁₀₈

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4752, then the Principal = ¹⁰⁰/₁₀₈ × 4752

= ^{100 × 4752}/₁₀₈

= ⁴⁷⁵²⁰⁰/₁₀₈

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

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

(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?

(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?

(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?

(8) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?

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