Simple Interest
Math MCQs

Question :    How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

Correct Answer  $5200

Solution & Explanation

Solution

Given,

Amount (A) = $5980

Rate of Simple Interest (R) = 3%

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

$5980 = P (1 + 3% × 5)

⇒ $5980 = P (1 + ³/₁₀₀ × 5)

⇒ $5980 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $5980 = P (1 + ¹⁵/₁₀₀)

⇒ $5980 = P (^{100 + 15}/₁₀₀)

⇒ $5980 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5980

⇒ P = ⁵⁹⁸⁰/_¹¹⁵/100

⇒ P = 5980 × ¹⁰⁰/₁₁₅

⇒ P = ^{5980 × 100}/₁₁₅

⇒ P = ⁵⁹⁸⁰⁰⁰/₁₁₅

⇒ P = $5200

Thus, the sum borrowed (P) = $5200 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 5980, then the Principal = ¹⁰⁰/₁₁₅ × 5980

= ^{100 × 5980}/₁₁₅

= ⁵⁹⁸⁰⁰⁰/₁₁₅

= 5200

Thus, Principal = $5200

Thus, the sum borrowed = $5200 Answer

Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.

(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(5) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(7) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(8) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.