Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $9520

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 = $9520 – $7000 = $2520

Thus, Simple Interest = $2520

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 × 2520}/_{7000 × 6}

= ²⁵²⁰⁰⁰/₄₂₀₀₀

= 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) = $7000

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

Simple Interest = $2520 (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 $7000

= ⁶/₁₀₀ × 7000

= ^{6 × 7000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $2520, then the time = ¹/₄₂₀ × 2520 years

= ^{1 × 2520}/₄₂₀ years

= ²⁵²⁰/₄₂₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?

(3) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(5) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?

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

(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.