Simple Interest
Math MCQs

Question :    How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $6375

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

$6375 = P (1 + 5% × 5)

⇒ $6375 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6375 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6375 = P (1 + ²⁵/₁₀₀)

⇒ $6375 = P (^{100 + 25}/₁₀₀)

⇒ $6375 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6375

⇒ P = ⁶³⁷⁵/_¹²⁵/100

⇒ P = 6375 × ¹⁰⁰/₁₂₅

⇒ P = ^{6375 × 100}/₁₂₅

⇒ P = ⁶³⁷⁵⁰⁰/₁₂₅

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 6375, then the Principal = ¹⁰⁰/₁₂₅ × 6375

= ^{100 × 6375}/₁₂₅

= ⁶³⁷⁵⁰⁰/₁₂₅

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(4) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(7) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

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

(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.