Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $7125

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$7125 = P (1 + 5% × 5)

⇒ $7125 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7125 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7125 = P (1 + ²⁵/₁₀₀)

⇒ $7125 = P (^{100 + 25}/₁₀₀)

⇒ $7125 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7125

⇒ P = ⁷¹²⁵/_¹²⁵/100

⇒ P = 7125 × ¹⁰⁰/₁₂₅

⇒ P = ^{7125 × 100}/₁₂₅

⇒ P = ⁷¹²⁵⁰⁰/₁₂₅

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7125, then the Principal = ¹⁰⁰/₁₂₅ × 7125

= ^{100 × 7125}/₁₂₅

= ⁷¹²⁵⁰⁰/₁₂₅

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?

(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?

(9) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.

(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.