Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 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) = 8% per annum

Amount (A) = $6364

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 = $6364 – $4300 = $2064

Thus, Simple Interest = $2064

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 × 2064}/_{4300 × 8}

= ²⁰⁶⁴⁰⁰/₃₄₄₀₀

= 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) = 8% per annum

Simple Interest = $2064 (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 = 8% of Principal

= 8% of $4300

= ⁸/₁₀₀ × 4300

= ^{8 × 4300}/₁₀₀

= ³⁴⁴⁰⁰/₁₀₀ = 344

Thus, simple Interest for 1 year = $344

Now,

∵ If the simple Interest is $344, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₄ years

∴ If the simple Interest is $2064, then the time = ¹/₃₄₄ × 2064 years

= ^{1 × 2064}/₃₄₄ years

= ²⁰⁶⁴/₃₄₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

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

(3) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(5) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.

(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.

(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.