Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6420

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

$6420 = P (1 + 4% × 5)

⇒ $6420 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6420 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6420 = P (1 + ²⁰/₁₀₀)

⇒ $6420 = P (^{100 + 20}/₁₀₀)

⇒ $6420 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6420

⇒ P = ⁶⁴²⁰/_¹²⁰/100

⇒ P = 6420 × ¹⁰⁰/₁₂₀

⇒ P = ^{6420 × 100}/₁₂₀

⇒ P = ⁶⁴²⁰⁰⁰/₁₂₀

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 6420, then the Principal = ¹⁰⁰/₁₂₀ × 6420

= ^{100 × 6420}/₁₂₀

= ⁶⁴²⁰⁰⁰/₁₂₀

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?

(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

(4) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(5) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(10) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.