Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $6880

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 = $6880 – $4300 = $2580

Thus, Simple Interest = $2580

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 × 2580}/_{4300 × 10}

= ²⁵⁸⁰⁰⁰/₄₃₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4300

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $2580 (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 = 10% of Principal

= 10% of $4300

= ¹⁰/₁₀₀ × 4300

= ^{10 × 4300}/₁₀₀

= ⁴³⁰⁰⁰/₁₀₀ = 430

Thus, simple Interest for 1 year = $430

Now,

∵ If the simple Interest is $430, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₀ years

∴ If the simple Interest is $2580, then the time = ¹/₄₃₀ × 2580 years

= ^{1 × 2580}/₄₃₀ years

= ²⁵⁸⁰/₄₃₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(2) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(4) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.