Simple Interest
MCQs Math

Question:     Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $9120

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 = $9120 – $5700 = $3420

Thus, Simple Interest = $3420

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 × 3420}/_{5700 × 6}

= ³⁴²⁰⁰⁰/₃₄₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5700

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

Simple Interest = $3420 (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 $5700

= ⁶/₁₀₀ × 5700

= ^{6 × 5700}/₁₀₀

= ³⁴²⁰⁰/₁₀₀ = 342

Thus, simple Interest for 1 year = $342

Now,

∵ If the simple Interest is $342, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₂ years

∴ If the simple Interest is $3420, then the time = ¹/₃₄₂ × 3420 years

= ^{1 × 3420}/₃₄₂ years

= ³⁴²⁰/₃₄₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(2) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(4) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(6) If Joseph paid $4144 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 if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?

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

(10) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.