Question

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

150,000(1.012)^2t

What is the annual rate of interest for this situation?

2.4%
0.6%
0.06%
1.2%

Answer 1

The amount accrued in a compound interest is given by the following formula:

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

The following expression gives Nelson's payable amount after t years:

150,000(1.012)^2t

Compare the two expressions:

A = 150,000(1.012)^2t 

A = P (1 + r/n) ^(nt)

From the expression, you can see that:

(1 + r/n) = 1.012

Therefore, 

r/n  = 1.012 - 1

r/n = 0.012

r = 0.012n

n = 2, since Nelson's interest, is compounded semiannually.

Therefore, r = 0.012 × 2 = 0.024

Since r is in decimal form, we convert this to %

0.012 × 100%  = 2.4%


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Answer 2

Answer:

idk

Step-by-step explanation: