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 if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.

(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(3) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?

(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?

(8) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.