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) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

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

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

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

(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.

(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.