Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $9200

Rate of Simple Interest (R) = 3%

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

$9200 = P (1 + 3% × 5)

⇒ $9200 = P (1 + ³/₁₀₀ × 5)

⇒ $9200 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9200 = P (1 + ¹⁵/₁₀₀)

⇒ $9200 = P (^{100 + 15}/₁₀₀)

⇒ $9200 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9200

⇒ P = ⁹²⁰⁰/_¹¹⁵/100

⇒ P = 9200 × ¹⁰⁰/₁₁₅

⇒ P = ^{9200 × 100}/₁₁₅

⇒ P = ⁹²⁰⁰⁰⁰/₁₁₅

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 9200, then the Principal = ¹⁰⁰/₁₁₅ × 9200

= ^{100 × 9200}/₁₁₅

= ⁹²⁰⁰⁰⁰/₁₁₅

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(5) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

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

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(10) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.