Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8528

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 = $8528 – $5200 = $3328

Thus, Simple Interest = $3328

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 × 3328}/_{5200 × 8}

= ³³²⁸⁰⁰/₄₁₆₀₀

= 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) = $5200

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3328 (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 = 8% of Principal

= 8% of $5200

= ⁸/₁₀₀ × 5200

= ^{8 × 5200}/₁₀₀

= ⁴¹⁶⁰⁰/₁₀₀ = 416

Thus, simple Interest for 1 year = $416

Now,

∵ If the simple Interest is $416, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₆ years

∴ If the simple Interest is $3328, then the time = ¹/₄₁₆ × 3328 years

= ^{1 × 3328}/₄₁₆ years

= ³³²⁸/₄₁₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(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) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(7) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(8) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.

(10) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?