Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $11400

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 = $11400 – $5700 = $5700

Thus, Simple Interest = $5700

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 × 5700}/_{5700 × 10}

= ⁵⁷⁰⁰⁰⁰/₅₇₀₀₀

= 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) = 10% per annum

Simple Interest = $5700 (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 $5700

= ¹⁰/₁₀₀ × 5700

= ^{10 × 5700}/₁₀₀

= ⁵⁷⁰⁰⁰/₁₀₀ = 570

Thus, simple Interest for 1 year = $570

Now,

∵ If the simple Interest is $570, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₇₀ years

∴ If the simple Interest is $5700, then the time = ¹/₅₇₀ × 5700 years

= ^{1 × 5700}/₅₇₀ years

= ⁵⁷⁰⁰/₅₇₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.

(2) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?

(4) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(5) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.

(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?

(8) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?