Simple Interest
Math MCQs

Question :    How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

Correct Answer  $6700

Solution & Explanation

Solution

Given,

Amount (A) = $7370

Rate of Simple Interest (R) = 2%

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

$7370 = P (1 + 2% × 5)

⇒ $7370 = P (1 + ²/₁₀₀ × 5)

⇒ $7370 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7370 = P (1 + ¹⁰/₁₀₀)

⇒ $7370 = P (^{100 + 10}/₁₀₀)

⇒ $7370 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7370

⇒ P = ⁷³⁷⁰/_¹¹⁰/100

⇒ P = 7370 × ¹⁰⁰/₁₁₀

⇒ P = ^{7370 × 100}/₁₁₀

⇒ P = ⁷³⁷⁰⁰⁰/₁₁₀

⇒ P = $6700

Thus, the sum borrowed (P) = $6700 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7370, then the Principal = ¹⁰⁰/₁₁₀ × 7370

= ^{100 × 7370}/₁₁₀

= ⁷³⁷⁰⁰⁰/₁₁₀

= 6700

Thus, Principal = $6700

Thus, the sum borrowed = $6700 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.

(3) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?

(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?

(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.

(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.