Simple Interest
Math MCQs

Question :    If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5880

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

$5880 = P (1 + 5% × 4)

⇒ $5880 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5880 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5880 = P (1 + ²⁰/₁₀₀)

⇒ $5880 = P (^{100 + 20}/₁₀₀)

⇒ $5880 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5880

⇒ P = ⁵⁸⁸⁰/_¹²⁰/100

⇒ P = 5880 × ¹⁰⁰/₁₂₀

⇒ P = ^{5880 × 100}/₁₂₀

⇒ P = ⁵⁸⁸⁰⁰⁰/₁₂₀

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 5880, then the Principal = ¹⁰⁰/₁₂₀ × 5880

= ^{100 × 5880}/₁₂₀

= ⁵⁸⁸⁰⁰⁰/₁₂₀

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?

(2) 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?

(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?

(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(7) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.

(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?

(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.