Simple Interest
Math MCQs

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 & 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) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?

(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(5) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

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

(7) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(8) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.