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 $9685 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $9685

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 = $9685 – $6500 = $3185

Thus, Simple Interest = $3185

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 × 3185}/_{6500 × 7}

= ³¹⁸⁵⁰⁰/₄₅₅₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $3185 (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 $3185, then the time = ¹/₄₅₅ × 3185 years

= ^{1 × 3185}/₄₅₅ years

= ³¹⁸⁵/₄₅₅ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(3) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(8) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(9) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?

(10) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.