Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $7125

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

$7125 = P (1 + 5% × 5)

⇒ $7125 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7125 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7125 = P (1 + ²⁵/₁₀₀)

⇒ $7125 = P (^{100 + 25}/₁₀₀)

⇒ $7125 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7125

⇒ P = ⁷¹²⁵/_¹²⁵/100

⇒ P = 7125 × ¹⁰⁰/₁₂₅

⇒ P = ^{7125 × 100}/₁₂₅

⇒ P = ⁷¹²⁵⁰⁰/₁₂₅

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 7125, then the Principal = ¹⁰⁰/₁₂₅ × 7125

= ^{100 × 7125}/₁₂₅

= ⁷¹²⁵⁰⁰/₁₂₅

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(2) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.

(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

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