Simple Interest
Math MCQs

Question :    If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4536

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

$4536 = P (1 + 2% × 4)

⇒ $4536 = P (1 + ²/₁₀₀ × 4)

⇒ $4536 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4536 = P (1 + ⁸/₁₀₀)

⇒ $4536 = P (^{100 + 8}/₁₀₀)

⇒ $4536 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4536

⇒ P = ⁴⁵³⁶/_¹⁰⁸/100

⇒ P = 4536 × ¹⁰⁰/₁₀₈

⇒ P = ^{4536 × 100}/₁₀₈

⇒ P = ⁴⁵³⁶⁰⁰/₁₀₈

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 4536, then the Principal = ¹⁰⁰/₁₀₈ × 4536

= ^{100 × 4536}/₁₀₈

= ⁴⁵³⁶⁰⁰/₁₀₈

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.

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

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?

(6) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(8) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(9) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?