Question 1

What is the sum of the first 6 terms of an arithmetic progression when a = 3 and d = 4?

Accepted Answer

The sum of the first n terms of an arithmetic progression can be found using the formula $S_n = \frac{n}{2}[2a + (n-1)d]$, where $a$ is the first term, $d$ is the common difference, and $n$ is the number of terms. Substituting $a = 3$, $d = 4$, and $n = 6$ into the formula gives $S_6 = \frac{6}{2}[2(3) + (6-1)4] = 3[6 + 20] = 3 \times 26 = 78$.

Question 2

A Kenyan company takes a loan of 100,000 Kenyan Shillings (KES) - what term is used to refer to this amount?

Accepted Answer

The term "Principal amount" refers to the initial sum of money borrowed in a loan, before any interest or fees are added.

Question 3

What is the 5th term of a geometric progression when a = 2 and r = 3?

Accepted Answer

The 5th term of a geometric progression is given by $a \cdot r^{(n-1)}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the term number. Here, $a = 2$, $r = 3$, and $n = 5$, so the 5th term is $2 \cdot 3^{(5-1)} = 2 \cdot 3^4 = 2 \cdot 81 = 162$.

Question 4

What is the Annual Percentage Rate (APR) of a loan with Nominal Rate of 8% and a Compounding Period of 3 months (n = 4) (1 decimal place)?

Accepted Answer

The APR can be calculated using the formula for the effective annual rate (EAR), which accounts for compounding within the year. The formula is $EAR = (1 + \frac{r}{n})^n - 1$, where $r$ is the nominal rate (expressed as a decimal) and $n$ is the number of compounding periods per year. Plugging in the given values, $EAR = (1 + \frac{0.08}{4})^4 - 1 = (1 + 0.02)^4 - 1 \approx 0.0824$ or 8.2% when converted to a percentage.

Question 5

What is the 7th term of an arithmetic progression when a = 5 and d = 3?

Accepted Answer

The 7th term of an arithmetic progression can be found using the formula $a_n = a + (n-1)d$, where $a$ is the first term, $d$ is the common difference, and $n$ is the term number. Substituting $a = 5$, $d = 3$, and $n = 7$, we get $a_7 = 5 + (7-1)3 = 5 + 18 = 23$.

Question 6

What is the sum of the first 8 terms of a geometric progression when a = 4 and r = 2?

Accepted Answer

The answer of What is the sum of the first...

Question 7

A law firm in Oman purchases a new car for partners' use. Its original value is 19,000 Omani Rial (OMR) and it will depreciate by 15% per year. How much will it be worth after 3 years (to the nearest OMR)?

Accepted Answer

The answer of A law firm in Oman purchases a...

Question 8

A clothing company in Pakistan purchases a new machine worth 1.5 million Pakistani Rupees (PKR). In 5 years it will be worth PKR 300,000. Assuming a straight line depreciation, by how much should its value be depreciated each year?

Accepted Answer

The straight line depreciation per year is calculated by subtracting the salvage value (value at the end of its useful life) from the initial cost and then dividing by the number of years of useful life. Here, (1,500,000 - 300,000) / 5 = 1,200,000 / 5 = PKR 240,000 per year.

Question 9

A transport company in the Philippines borrows 60,000 Philippine Pesos (PHP) at an interest rate of 6% per year. After 3 years, assuming they have paid nothing back, what it the value of Accrued Amount (to the nearest PHP)?

Accepted Answer

The Accrued Amount can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt). Here, P = 60,000, r = 0.06, n = 1, and t = 3. Plugging in these values, A = 60,000(1 + 0.06)^3 = 71,461.

Question 10

A Turkish company has a computer with a depreciated value (D) of 1,200 Turkish Lira (TRY) after 4 years depreciation at 9%. What was its original book value (B) (to nearest TRY)?

Accepted Answer

The answer of A Turkish company has a computer with...

Quiz 21: Interest and Depreciation

What is the sum of the first 6 terms of an arithmetic progression when a = 3 and d = 4?

A Kenyan company takes a loan of 100,000 Kenyan Shillings (KES) - what term is used to refer to this amount?

What is the 5th term of a geometric progression when a = 2 and r = 3?

What is the Annual Percentage Rate (APR) of a loan with Nominal Rate of 8% and a Compounding Period of 3 months (n = 4) (1 decimal place) ?

What is the 7th term of an arithmetic progression when a = 5 and d = 3?

What is the sum of the first 8 terms of a geometric progression when a = 4 and r = 2?

A law firm in Oman purchases a new car for partners' use. Its original value is 19,000 Omani Rial (OMR) and it will depreciate by 15% per year. How much will it be worth after 3 years (to the nearest OMR) ?

A clothing company in Pakistan purchases a new machine worth 1.5 million Pakistani Rupees (PKR) . In 5 years it will be worth PKR 300,000. Assuming a straight line depreciation, by how much should its value be depreciated each year?

A transport company in the Philippines borrows 60,000 Philippine Pesos (PHP) at an interest rate of 6% per year. After 3 years, assuming they have paid nothing back, what it the value of Accrued Amount (to the nearest PHP) ?

A Turkish company has a computer with a depreciated value (D) of 1,200 Turkish Lira (TRY) after 4 years depreciation at 9%. What was its original book value (B) (to nearest TRY) ?