Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $9120

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

$9120 = P (1 + 4% × 5)

⇒ $9120 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9120 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9120 = P (1 + ²⁰/₁₀₀)

⇒ $9120 = P (^{100 + 20}/₁₀₀)

⇒ $9120 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9120

⇒ P = ⁹¹²⁰/_¹²⁰/100

⇒ P = 9120 × ¹⁰⁰/₁₂₀

⇒ P = ^{9120 × 100}/₁₂₀

⇒ P = ⁹¹²⁰⁰⁰/₁₂₀

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 9120, then the Principal = ¹⁰⁰/₁₂₀ × 9120

= ^{100 × 9120}/₁₂₀

= ⁹¹²⁰⁰⁰/₁₂₀

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.

(2) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(7) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.