Simple Interest
Math MCQs

Question :    How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?

Correct Answer  $6000

Solution & Explanation

Solution

Given,

Amount (A) = $7500

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$7500 = P (1 + 5% × 5)

⇒ $7500 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7500 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7500 = P (1 + ²⁵/₁₀₀)

⇒ $7500 = P (^{100 + 25}/₁₀₀)

⇒ $7500 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7500

⇒ P = ⁷⁵⁰⁰/_¹²⁵/100

⇒ P = 7500 × ¹⁰⁰/₁₂₅

⇒ P = ^{7500 × 100}/₁₂₅

⇒ P = ⁷⁵⁰⁰⁰⁰/₁₂₅

⇒ P = $6000

Thus, the sum borrowed (P) = $6000 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7500, then the Principal = ¹⁰⁰/₁₂₅ × 7500

= ^{100 × 7500}/₁₂₅

= ⁷⁵⁰⁰⁰⁰/₁₂₅

= 6000

Thus, Principal = $6000

Thus, the sum borrowed = $6000 Answer

Similar Questions

(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?

(3) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?

(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(9) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.