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 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?

(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?

(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(6) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.