Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $7020

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

$7020 = P (1 + 4% × 5)

⇒ $7020 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7020 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7020 = P (1 + ²⁰/₁₀₀)

⇒ $7020 = P (^{100 + 20}/₁₀₀)

⇒ $7020 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7020

⇒ P = ⁷⁰²⁰/_¹²⁰/100

⇒ P = 7020 × ¹⁰⁰/₁₂₀

⇒ P = ^{7020 × 100}/₁₂₀

⇒ P = ⁷⁰²⁰⁰⁰/₁₂₀

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 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 7020, then the Principal = ¹⁰⁰/₁₂₀ × 7020

= ^{100 × 7020}/₁₂₀

= ⁷⁰²⁰⁰⁰/₁₂₀

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.

(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(8) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.