Simple Interest
Math MCQs

Question :    How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?

Correct Answer  $6600

Solution & Explanation

Solution

Given,

Amount (A) = $8250

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

$8250 = P (1 + 5% × 5)

⇒ $8250 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8250 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8250 = P (1 + ²⁵/₁₀₀)

⇒ $8250 = P (^{100 + 25}/₁₀₀)

⇒ $8250 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8250

⇒ P = ⁸²⁵⁰/_¹²⁵/100

⇒ P = 8250 × ¹⁰⁰/₁₂₅

⇒ P = ^{8250 × 100}/₁₂₅

⇒ P = ⁸²⁵⁰⁰⁰/₁₂₅

⇒ P = $6600

Thus, the sum borrowed (P) = $6600 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 8250, then the Principal = ¹⁰⁰/₁₂₅ × 8250

= ^{100 × 8250}/₁₂₅

= ⁸²⁵⁰⁰⁰/₁₂₅

= 6600

Thus, Principal = $6600

Thus, the sum borrowed = $6600 Answer

Similar Questions

(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?

(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.