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) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(4) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

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

(7) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.