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 $9804 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $9804

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 = $9804 – $5700 = $4104

Thus, Simple Interest = $4104

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 × 4104}/_{5700 × 8}

= ⁴¹⁰⁴⁰⁰/₄₅₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $4104 (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 $4104, then the time = ¹/₄₅₆ × 4104 years

= ^{1 × 4104}/₄₅₆ years

= ⁴¹⁰⁴/₄₅₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(9) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.