Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $8150

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 = $8150 – $5000 = $3150

Thus, Simple Interest = $3150

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 × 3150}/_{5000 × 7}

= ³¹⁵⁰⁰⁰/₃₅₀₀₀

= 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) = $5000

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

Simple Interest = $3150 (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 $5000

= ⁷/₁₀₀ × 5000

= ^{7 × 5000}/₁₀₀

= ³⁵⁰⁰⁰/₁₀₀ = 350

Thus, simple Interest for 1 year = $350

Now,

∵ If the simple Interest is $350, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₀ years

∴ If the simple Interest is $3150, then the time = ¹/₃₅₀ × 3150 years

= ^{1 × 3150}/₃₅₀ years

= ³¹⁵⁰/₃₅₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(3) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.