Simple Interest
Math MCQs

Question :    Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5488

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$5488 = P (1 + 4% × 3)

⇒ $5488 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5488 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5488 = P (1 + ¹²/₁₀₀)

⇒ $5488 = P (^{100 + 12}/₁₀₀)

⇒ $5488 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5488

⇒ P = ⁵⁴⁸⁸/_¹¹²/100

⇒ P = 5488 × ¹⁰⁰/₁₁₂

⇒ P = ^{5488 × 100}/₁₁₂

⇒ P = ⁵⁴⁸⁸⁰⁰/₁₁₂

⇒ 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 = 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5488, then the Principal = ¹⁰⁰/₁₁₂ × 5488

= ^{100 × 5488}/₁₁₂

= ⁵⁴⁸⁸⁰⁰/₁₁₂

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?

(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?

(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.