Suppose 300 was deposited into one of five bank accounts and

Suppose $300 was deposited into one of five bank accounts and t is time in years. Give the annual nominal rate and how it is being compounded, then give the effective annual rate. B = 300(1.05)^t % compounded r_e % per year B = 300(1.01)^12t % compounded r_e % per year B = 300(0.8)^t % compounded r_e % per year B = 300(0.97)^4t% compounded r_e % per year B = 300e^0.2t % compounded r_e % per year

Solution

We know compound interest formula A = P(1+r/n)^nt , where P is the deposited amount, r is the rate of interest, n is the number of instalments per year, t is the number of years.

a) B= 300(1.05)^t.

It can be written as B = 300 ( 1+ 0.05 )^t.

Therefore, P= $300, r/n = 0.05, and nt = t.

Because nt =t therefore, n=1. It shows that there would be only one installment per year.

Therefore we could also say r = 0.05 that is 5%.

Therefore, Annual Nominal Rate = 5%.

Effective annual interest rate can be found by formula

r= (1+r/n)^nt -1 = (1+0.05/1)^1*1-1 = 1.05 -1 = 0.05 = 5%

So, for (a) part 5% compounded annually and effective annual rate would also be 5%.

b) B= 300(1.01)^12t

It can be written as B = 300 ( 1+ 0.01 )^12*t.

Therefore, P= $300, r/n = 0.01, and nt = 12t.

Because nt =12t therefore, n=12. It shows that there would be only 12 installments per year.

Therefore we could also say r/n = 0.01.

Plugging n=12, r/12 = 0.01.

Therefore, r= 12* 0.01 = 0.12 that is 12%.

Effective annual interest rate = (1+0.12/12)^12*1-1 =(1.01)^12 -1= 0.12683 that is 12.683%

So, for (b) part 5% compounded monthly and effective annual rate would be 12.683%.

c) B= 300(1.08)^t

It can be written as B = 300 ( 1+ 0.08 )^1*t.

Therefore, P= $300, r/n = 0.08, and nt = t.

Because nt =t therefore, n=1. It shows that there would be only 1 installments per year.

Therefore we could also say r/n = 0.08.

Plugging n=1, r/1= 0.08.

Therefore, r= 1* 0.08 = 0.08 that is 8%.

Effective annual interest rate = (1+0.08/1)^1-1 =(1.08)^1 -1= 0.08 that is 8%

So, for (c) part 8% compounded annually and effective annual rate would also be 8%.

d) B= 300(0.97)^4t

It can be written as B = 300 ( 0+ 0.97 )^4*t.

Therefore, P= $300, r/n = 0.97-1.00= -0.03 , and nt = 4t.

Because nt =4t therefore, n=4. It shows that there would be only 4 installments per year (compounded quarterly).

Therefore we could also say r/n = -0.03.

Plugging n=4, r/4 = -0.03.

Therefore, r= 4* -0.03 = -0.12 that is -12%. Depreciate at 12%.

Effective annual interest rate = (1-0.12/4)^4*1-1 = -0.11471 that is -11.471%

So, for (d) part Depreciating at 12% compounded quartely and effective annual rate would be -11.471%.