Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $10140

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 = $10140 – $6500 = $3640

Thus, Simple Interest = $3640

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 × 3640}/_{6500 × 7}

= ³⁶⁴⁰⁰⁰/₄₅₅₀₀

= 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) = $6500

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

Simple Interest = $3640 (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 $6500

= ⁷/₁₀₀ × 6500

= ^{7 × 6500}/₁₀₀

= ⁴⁵⁵⁰⁰/₁₀₀ = 455

Thus, simple Interest for 1 year = $455

Now,

∵ If the simple Interest is $455, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₅ years

∴ If the simple Interest is $3640, then the time = ¹/₄₅₅ × 3640 years

= ^{1 × 3640}/₄₅₅ years

= ³⁶⁴⁰/₄₅₅ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?

(2) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.

(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(5) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.

(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.