Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9656

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 = $9656 – $6800 = $2856

Thus, Simple Interest = $2856

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 × 2856}/_{6800 × 6}

= ²⁸⁵⁶⁰⁰/₄₀₈₀₀

= 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) = $6800

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2856 (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 = 6% of Principal

= 6% of $6800

= ⁶/₁₀₀ × 6800

= ^{6 × 6800}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $2856, then the time = ¹/₄₀₈ × 2856 years

= ^{1 × 2856}/₄₀₈ years

= ²⁸⁵⁶/₄₀₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(3) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?

(7) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.

(9) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.