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 Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.

(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(6) 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.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(8) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?

(10) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.