Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $9750

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

$9750 = P (1 + 5% × 5)

⇒ $9750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9750 = P (1 + ²⁵/₁₀₀)

⇒ $9750 = P (^{100 + 25}/₁₀₀)

⇒ $9750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9750

⇒ P = ⁹⁷⁵⁰/_¹²⁵/100

⇒ P = 9750 × ¹⁰⁰/₁₂₅

⇒ P = ^{9750 × 100}/₁₂₅

⇒ P = ⁹⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $7800

Thus, the sum borrowed (P) = $7800 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 9750, then the Principal = ¹⁰⁰/₁₂₅ × 9750

= ^{100 × 9750}/₁₂₅

= ⁹⁷⁵⁰⁰⁰/₁₂₅

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.

(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(8) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?

(9) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(10) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.