Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $8280

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 = $8280 – $4600 = $3680

Thus, Simple Interest = $3680

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 × 3680}/_{4600 × 10}

= ³⁶⁸⁰⁰⁰/₄₆₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4600

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

Simple Interest = $3680 (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 $4600

= ¹⁰/₁₀₀ × 4600

= ^{10 × 4600}/₁₀₀

= ⁴⁶⁰⁰⁰/₁₀₀ = 460

Thus, simple Interest for 1 year = $460

Now,

∵ If the simple Interest is $460, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₀ years

∴ If the simple Interest is $3680, then the time = ¹/₄₆₀ × 3680 years

= ^{1 × 3680}/₄₆₀ years

= ³⁶⁸⁰/₄₆₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(4) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.

(8) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?

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

(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.