Simple Interest
Math MCQs

Question :    If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4620

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

$4620 = P (1 + 5% × 4)

⇒ $4620 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4620 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4620 = P (1 + ²⁰/₁₀₀)

⇒ $4620 = P (^{100 + 20}/₁₀₀)

⇒ $4620 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4620

⇒ P = ⁴⁶²⁰/_¹²⁰/100

⇒ P = 4620 × ¹⁰⁰/₁₂₀

⇒ P = ^{4620 × 100}/₁₂₀

⇒ P = ⁴⁶²⁰⁰⁰/₁₂₀

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 4620, then the Principal = ¹⁰⁰/₁₂₀ × 4620

= ^{100 × 4620}/₁₂₀

= ⁴⁶²⁰⁰⁰/₁₂₀

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.

(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(6) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

(7) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.

(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?