Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $7620

Rate of Simple Interest (R) = 4%

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

$7620 = P (1 + 4% × 5)

⇒ $7620 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7620 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7620 = P (1 + ²⁰/₁₀₀)

⇒ $7620 = P (^{100 + 20}/₁₀₀)

⇒ $7620 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7620

⇒ P = ⁷⁶²⁰/_¹²⁰/100

⇒ P = 7620 × ¹⁰⁰/₁₂₀

⇒ P = ^{7620 × 100}/₁₂₀

⇒ P = ⁷⁶²⁰⁰⁰/₁₂₀

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7620, then the Principal = ¹⁰⁰/₁₂₀ × 7620

= ^{100 × 7620}/₁₂₀

= ⁷⁶²⁰⁰⁰/₁₂₀

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.

(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?

(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(4) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.

(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.