Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $8236

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 = $8236 – $5800 = $2436

Thus, Simple Interest = $2436

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 × 2436}/_{5800 × 7}

= ²⁴³⁶⁰⁰/₄₀₆₀₀

= 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) = $5800

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

Simple Interest = $2436 (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 $5800

= ⁷/₁₀₀ × 5800

= ^{7 × 5800}/₁₀₀

= ⁴⁰⁶⁰⁰/₁₀₀ = 406

Thus, simple Interest for 1 year = $406

Now,

∵ If the simple Interest is $406, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₆ years

∴ If the simple Interest is $2436, then the time = ¹/₄₀₆ × 2436 years

= ^{1 × 2436}/₄₀₆ years

= ²⁴³⁶/₄₀₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(3) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(6) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

(7) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.

(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?