Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $7740

Rate of Simple Interest (R) = 4%

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

$7740 = P (1 + 4% × 5)

⇒ $7740 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7740 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7740 = P (1 + ²⁰/₁₀₀)

⇒ $7740 = P (^{100 + 20}/₁₀₀)

⇒ $7740 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7740

⇒ P = ⁷⁷⁴⁰/_¹²⁰/100

⇒ P = 7740 × ¹⁰⁰/₁₂₀

⇒ P = ^{7740 × 100}/₁₂₀

⇒ P = ⁷⁷⁴⁰⁰⁰/₁₂₀

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7740, then the Principal = ¹⁰⁰/₁₂₀ × 7740

= ^{100 × 7740}/₁₂₀

= ⁷⁷⁴⁰⁰⁰/₁₂₀

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.

(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(7) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.

(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(10) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?