Simple Interest
Math MCQs

Question :    How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?

Correct Answer  $5600

Solution & Explanation

Solution

Given,

Amount (A) = $7000

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

$7000 = P (1 + 5% × 5)

⇒ $7000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7000 = P (1 + ²⁵/₁₀₀)

⇒ $7000 = P (^{100 + 25}/₁₀₀)

⇒ $7000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7000

⇒ P = ⁷⁰⁰⁰/_¹²⁵/100

⇒ P = 7000 × ¹⁰⁰/₁₂₅

⇒ P = ^{7000 × 100}/₁₂₅

⇒ P = ⁷⁰⁰⁰⁰⁰/₁₂₅

⇒ P = $5600

Thus, the sum borrowed (P) = $5600 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 7000, then the Principal = ¹⁰⁰/₁₂₅ × 7000

= ^{100 × 7000}/₁₂₅

= ⁷⁰⁰⁰⁰⁰/₁₂₅

= 5600

Thus, Principal = $5600

Thus, the sum borrowed = $5600 Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(2) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?

(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.

(4) 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.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(9) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?