Simple Interest
Math MCQs

Question :    How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $9375

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

$9375 = P (1 + 5% × 5)

⇒ $9375 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9375 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9375 = P (1 + ²⁵/₁₀₀)

⇒ $9375 = P (^{100 + 25}/₁₀₀)

⇒ $9375 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9375

⇒ P = ⁹³⁷⁵/_¹²⁵/100

⇒ P = 9375 × ¹⁰⁰/₁₂₅

⇒ P = ^{9375 × 100}/₁₂₅

⇒ P = ⁹³⁷⁵⁰⁰/₁₂₅

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 9375, then the Principal = ¹⁰⁰/₁₂₅ × 9375

= ^{100 × 9375}/₁₂₅

= ⁹³⁷⁵⁰⁰/₁₂₅

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.

(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(4) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.

(6) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?

(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.