Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $10720

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 = $10720 – $6700 = $4020

Thus, Simple Interest = $4020

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 × 4020}/_{6700 × 6}

= ⁴⁰²⁰⁰⁰/₄₀₂₀₀

= 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) = $6700

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

Simple Interest = $4020 (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 $6700

= ⁶/₁₀₀ × 6700

= ^{6 × 6700}/₁₀₀

= ⁴⁰²⁰⁰/₁₀₀ = 402

Thus, simple Interest for 1 year = $402

Now,

∵ If the simple Interest is $402, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₂ years

∴ If the simple Interest is $4020, then the time = ¹/₄₀₂ × 4020 years

= ^{1 × 4020}/₄₀₂ years

= ⁴⁰²⁰/₄₀₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?

(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?

(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(5) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.

(8) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.

(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?

(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?