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) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

(2) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(4) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(6) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(9) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.