Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7380

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 = $7380 – $4100 = $3280

Thus, Simple Interest = $3280

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 × 3280}/_{4100 × 10}

= ³²⁸⁰⁰⁰/₄₁₀₀₀

= 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) = $4100

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3280 (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 = 10% of Principal

= 10% of $4100

= ¹⁰/₁₀₀ × 4100

= ^{10 × 4100}/₁₀₀

= ⁴¹⁰⁰⁰/₁₀₀ = 410

Thus, simple Interest for 1 year = $410

Now,

∵ If the simple Interest is $410, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₀ years

∴ If the simple Interest is $3280, then the time = ¹/₄₁₀ × 3280 years

= ^{1 × 3280}/₄₁₀ years

= ³²⁸⁰/₄₁₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.

(3) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(4) 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.

(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?

(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?

(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(10) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.