Simple Interest
Math MCQs

Question :    How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $7375

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

$7375 = P (1 + 5% × 5)

⇒ $7375 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7375 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7375 = P (1 + ²⁵/₁₀₀)

⇒ $7375 = P (^{100 + 25}/₁₀₀)

⇒ $7375 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7375

⇒ P = ⁷³⁷⁵/_¹²⁵/100

⇒ P = 7375 × ¹⁰⁰/₁₂₅

⇒ P = ^{7375 × 100}/₁₂₅

⇒ P = ⁷³⁷⁵⁰⁰/₁₂₅

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 7375, then the Principal = ¹⁰⁰/₁₂₅ × 7375

= ^{100 × 7375}/₁₂₅

= ⁷³⁷⁵⁰⁰/₁₂₅

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.

(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(3) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.

(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?

(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.