Simple Interest
Math MCQs

Question :    How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

Correct Answer  $6200

Solution & Explanation

Solution

Given,

Amount (A) = $7750

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

$7750 = P (1 + 5% × 5)

⇒ $7750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7750 = P (1 + ²⁵/₁₀₀)

⇒ $7750 = P (^{100 + 25}/₁₀₀)

⇒ $7750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7750

⇒ P = ⁷⁷⁵⁰/_¹²⁵/100

⇒ P = 7750 × ¹⁰⁰/₁₂₅

⇒ P = ^{7750 × 100}/₁₂₅

⇒ P = ⁷⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $6200

Thus, the sum borrowed (P) = $6200 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 7750, then the Principal = ¹⁰⁰/₁₂₅ × 7750

= ^{100 × 7750}/₁₂₅

= ⁷⁷⁵⁰⁰⁰/₁₂₅

= 6200

Thus, Principal = $6200

Thus, the sum borrowed = $6200 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(4) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(6) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.

(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.