Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $7987

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 = $7987 – $4900 = $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}/_{4900 × 7}

= ³⁰⁸⁷⁰⁰/₃₄₃₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4900

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 $4900

= ⁷/₁₀₀ × 4900

= ^{7 × 4900}/₁₀₀

= ³⁴³⁰⁰/₁₀₀ = 343

Thus, simple Interest for 1 year = $343

Now,

∵ If the simple Interest is $343, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₃ years

∴ If the simple Interest is $3087, then the time = ¹/₃₄₃ × 3087 years

= ^{1 × 3087}/₃₄₃ years

= ³⁰⁸⁷/₃₄₃ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?

(2) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?

(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(6) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.