Question

Given that d + (4) = 8%, find the equivalent rates for d, d(3), i, and i(6).

a) d = 2%, d(3) = 6%, i = 2%, i(6) = 12%
b) d = 4%, d(3) = 12%, i = 4%, i(6) = 24%
c) d = 6%, d(3) = 18%, i = 6%, i(6) = 36%
d) d = 8%, d(3) = 24%, i = 8%, i(6) = 48%

Answer 1

Using the initial equation d + (4) = 8%, we solve for d to get 4%. We then apply the simple additive rule to determine d(3) as 12% and similarly i as 4% and i(6) as 24%. Option b is the correct set of equivalent rates.

Step-by-step explanation:

The student is asking about the relationships between different rates of interest or discount rates and how these rates can be applied over different time periods. Initially, we're given an equation where d + (4) equals 8%. Here d represents a basic discount rate, and (4) seems to be an additive constant in this equation.

To solve for d, we can rearrange the equation given:

d = 8% - 4%

By calculating, we find d = 4%. From there, we can compound the discount rate over three periods to find d(3). Compounded interest is calculated as follows:

d(3) = d + d + d = 4% + 4% + 4% = 12%

Next, if we consider i to be the equivalent interest rate, we can assume it is the same as our discount rate d. Thus, i = 4%, and the compounded interest rate over 6 periods i(6) would be:

i(6) = i(3) + i(3) = 12% + 12% = 24%

Therefore, the correct answer is b) d = 4%, d(3) = 12%, i = 4%, i(6) = 24%.