Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6687.5

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

$6687.5 = P (1 + 5% × 5)

⇒ $6687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6687.5 = P (1 + ²⁵/₁₀₀)

⇒ $6687.5 = P (^{100 + 25}/₁₀₀)

⇒ $6687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6687.5

⇒ P = ^6687.5/_¹²⁵/100

⇒ P = 6687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6687.5 × 100}/₁₂₅

⇒ P = ⁶⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 6687.5, then the Principal = ¹⁰⁰/₁₂₅ × 6687.5

= ^{100 × 6687.5}/₁₂₅

= ⁶⁶⁸⁷⁵⁰/₁₂₅

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?

(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.