Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9387

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9387 – $6300 = $3087

Thus, Simple Interest = $3087

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3087}/_{6300 × 7}

= ³⁰⁸⁷⁰⁰/₄₄₁₀₀

= 7 years (using formula)

Thus, Time (T) = 7 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6300

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3087 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 7% of Principal

= 7% of $6300

= ⁷/₁₀₀ × 6300

= ^{7 × 6300}/₁₀₀

= ⁴⁴¹⁰⁰/₁₀₀ = 441

Thus, simple Interest for 1 year = $441

Now,

∵ If the simple Interest is $441, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₁ years

∴ If the simple Interest is $3087, then the time = ¹/₄₄₁ × 3087 years

= ^{1 × 3087}/₄₄₁ years

= ³⁰⁸⁷/₄₄₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?

(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.

(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?

(10) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?