Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $7062.5

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

$7062.5 = P (1 + 5% × 5)

⇒ $7062.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7062.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7062.5 = P (1 + ²⁵/₁₀₀)

⇒ $7062.5 = P (^{100 + 25}/₁₀₀)

⇒ $7062.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7062.5

⇒ P = ^7062.5/_¹²⁵/100

⇒ P = 7062.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7062.5 × 100}/₁₂₅

⇒ P = ⁷⁰⁶²⁵⁰/₁₂₅

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 7062.5, then the Principal = ¹⁰⁰/₁₂₅ × 7062.5

= ^{100 × 7062.5}/₁₂₅

= ⁷⁰⁶²⁵⁰/₁₂₅

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?

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

(3) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?

(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?