Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $8436

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 = $8436 – $5700 = $2736

Thus, Simple Interest = $2736

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 × 2736}/_{5700 × 8}

= ²⁷³⁶⁰⁰/₄₅₆₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 8% per annum

Simple Interest = $2736 (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 $5700

= ⁸/₁₀₀ × 5700

= ^{8 × 5700}/₁₀₀

= ⁴⁵⁶⁰⁰/₁₀₀ = 456

Thus, simple Interest for 1 year = $456

Now,

∵ If the simple Interest is $456, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₆ years

∴ If the simple Interest is $2736, then the time = ¹/₄₅₆ × 2736 years

= ^{1 × 2736}/₄₅₆ years

= ²⁷³⁶/₄₅₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(5) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

(6) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(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) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?