Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $11880

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 = $11880 – $6600 = $5280

Thus, Simple Interest = $5280

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 × 5280}/_{6600 × 10}

= ⁵²⁸⁰⁰⁰/₆₆₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6600

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

Simple Interest = $5280 (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 $6600

= ¹⁰/₁₀₀ × 6600

= ^{10 × 6600}/₁₀₀

= ⁶⁶⁰⁰⁰/₁₀₀ = 660

Thus, simple Interest for 1 year = $660

Now,

∵ If the simple Interest is $660, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₆₀ years

∴ If the simple Interest is $5280, then the time = ¹/₆₆₀ × 5280 years

= ^{1 × 5280}/₆₆₀ years

= ⁵²⁸⁰/₆₆₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.

(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(3) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(7) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(9) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?