Simple Interest
Math MCQs

Question :    How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

Correct Answer  $6150

Solution & Explanation

Solution

Given,

Amount (A) = $7380

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

$7380 = P (1 + 4% × 5)

⇒ $7380 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7380 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7380 = P (1 + ²⁰/₁₀₀)

⇒ $7380 = P (^{100 + 20}/₁₀₀)

⇒ $7380 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7380

⇒ P = ⁷³⁸⁰/_¹²⁰/100

⇒ P = 7380 × ¹⁰⁰/₁₂₀

⇒ P = ^{7380 × 100}/₁₂₀

⇒ P = ⁷³⁸⁰⁰⁰/₁₂₀

⇒ P = $6150

Thus, the sum borrowed (P) = $6150 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 7380, then the Principal = ¹⁰⁰/₁₂₀ × 7380

= ^{100 × 7380}/₁₂₀

= ⁷³⁸⁰⁰⁰/₁₂₀

= 6150

Thus, Principal = $6150

Thus, the sum borrowed = $6150 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.

(3) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(6) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?

(9) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?