Simple Interest
Math MCQs

Question :    If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $4020

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$4020 = P (1 + 5% × 4)

⇒ $4020 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4020 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4020 = P (1 + ²⁰/₁₀₀)

⇒ $4020 = P (^{100 + 20}/₁₀₀)

⇒ $4020 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4020

⇒ P = ⁴⁰²⁰/_¹²⁰/100

⇒ P = 4020 × ¹⁰⁰/₁₂₀

⇒ P = ^{4020 × 100}/₁₂₀

⇒ P = ⁴⁰²⁰⁰⁰/₁₂₀

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 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 4020, then the Principal = ¹⁰⁰/₁₂₀ × 4020

= ^{100 × 4020}/₁₂₀

= ⁴⁰²⁰⁰⁰/₁₂₀

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(8) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(10) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.