Simple Interest
Math MCQs

Question :    How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $9420

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

$9420 = P (1 + 4% × 5)

⇒ $9420 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9420 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9420 = P (1 + ²⁰/₁₀₀)

⇒ $9420 = P (^{100 + 20}/₁₀₀)

⇒ $9420 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9420

⇒ P = ⁹⁴²⁰/_¹²⁰/100

⇒ P = 9420 × ¹⁰⁰/₁₂₀

⇒ P = ^{9420 × 100}/₁₂₀

⇒ P = ⁹⁴²⁰⁰⁰/₁₂₀

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 9420, then the Principal = ¹⁰⁰/₁₂₀ × 9420

= ^{100 × 9420}/₁₂₀

= ⁹⁴²⁰⁰⁰/₁₂₀

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?

(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(9) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.