Question

Nelson took out a home loan that compounds interest semiannually. The following expression represents the payable amount after t years.

What is the annual rate of interest for this situation?

Answer 1

Amount accrued from compounded interest is calculated in the following manner: 

A = P (1 + r/n) ^(nt)

Where:

A = This is the principal amount plus interests earned,

P = This is the loan amount or the money deposited.

r = the annual interest rate in decimal

n = the number of times that interest is compounded per year ( in this case it is twice a year - semiannually)

t = This is the total number of years the money is invested or borrowed.

We can then use this formula to write an expression for the amount of money that will be accrued and consequently find the interest in a year.

If this is the payable amount after t years, then we can find the interest per year.

A = 150,000(1.012)^2t 

This means:

P  = 150,000

n= 2  (that is twice a year)

r = ? 

t = ?

A = P (1 + r/n) ^(nt).............. A = 150,000(1.012)^2t 

⇒ We can see from the two formulas, that the values in the brackets are equal:

(1 + r/n)  = (1.012)

1 + r/n  = 1.012

r/n = 1.012 - 1

r/n = 0.012

n = 2

∴ r/2 = 0.012


r  = 0.012 × 2

r = 0.024

Since r is the interest as a decimal, we can convert this to a percentage.

0.024 × 100 = 2.4 %

Therefore the interest payable per year, in this case, is 2.4 %

Answer 2

Answer:

456

Step-by-step explanation: