Simple Interest
Math MCQs

Question :    How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?

Correct Answer  $7900

Solution & Explanation

Solution

Given,

Amount (A) = $9085

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

$9085 = P (1 + 3% × 5)

⇒ $9085 = P (1 + ³/₁₀₀ × 5)

⇒ $9085 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9085 = P (1 + ¹⁵/₁₀₀)

⇒ $9085 = P (^{100 + 15}/₁₀₀)

⇒ $9085 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9085

⇒ P = ⁹⁰⁸⁵/_¹¹⁵/100

⇒ P = 9085 × ¹⁰⁰/₁₁₅

⇒ P = ^{9085 × 100}/₁₁₅

⇒ P = ⁹⁰⁸⁵⁰⁰/₁₁₅

⇒ P = $7900

Thus, the sum borrowed (P) = $7900 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 9085, then the Principal = ¹⁰⁰/₁₁₅ × 9085

= ^{100 × 9085}/₁₁₅

= ⁹⁰⁸⁵⁰⁰/₁₁₅

= 7900

Thus, Principal = $7900

Thus, the sum borrowed = $7900 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

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

(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.

(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?

(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.