Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6780

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

$6780 = P (1 + 4% × 5)

⇒ $6780 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6780 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6780 = P (1 + ²⁰/₁₀₀)

⇒ $6780 = P (^{100 + 20}/₁₀₀)

⇒ $6780 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6780

⇒ P = ⁶⁷⁸⁰/_¹²⁰/100

⇒ P = 6780 × ¹⁰⁰/₁₂₀

⇒ P = ^{6780 × 100}/₁₂₀

⇒ P = ⁶⁷⁸⁰⁰⁰/₁₂₀

⇒ 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 = 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 6780, then the Principal = ¹⁰⁰/₁₂₀ × 6780

= ^{100 × 6780}/₁₂₀

= ⁶⁷⁸⁰⁰⁰/₁₂₀

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(2) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(6) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?

(10) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?