Simple Interest
Math MCQs

Question :    How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

Correct Answer  $7900

Solution & Explanation

Solution

Given,

Amount (A) = $9480

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

$9480 = P (1 + 4% × 5)

⇒ $9480 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9480 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9480 = P (1 + ²⁰/₁₀₀)

⇒ $9480 = P (^{100 + 20}/₁₀₀)

⇒ $9480 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9480

⇒ P = ⁹⁴⁸⁰/_¹²⁰/100

⇒ P = 9480 × ¹⁰⁰/₁₂₀

⇒ P = ^{9480 × 100}/₁₂₀

⇒ P = ⁹⁴⁸⁰⁰⁰/₁₂₀

⇒ P = $7900

Thus, the sum borrowed (P) = $7900 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 9480, then the Principal = ¹⁰⁰/₁₂₀ × 9480

= ^{100 × 9480}/₁₂₀

= ⁹⁴⁸⁰⁰⁰/₁₂₀

= 7900

Thus, Principal = $7900

Thus, the sum borrowed = $7900 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(2) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?

(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(9) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.