Answer:
C 12.80%
Explanation:
You want the interest rate that, convertible monthly, will allow an annuity immediate to pay $600 quarterly for 12 years at a cost of $15,000.
Interest rate
The relationship between the variables of an annuity immediate is ...
P = A(1 -(1 +i)^-n)(1 +i)/i
where i is the interest rate per payment period, n is the number of payments of amount A, and P is the cost of the annuity.
Since payments are quarterly and interest is converted monthly, the annual rate r relates to the i in the formula by ...
(1 +i)^4 = (1 +r/12)^12
We need to solve for r that satisfies both of these equations when ...
P = 15000, A = 600, n = 48
The solution requires iteration. Financial calculators and spreadsheets are capable of this. The result is shown in the attachment.
The nominal interest rate is 12.79%. The closest answer choice is 12.80%.
__
Additional comment
"Converted" in this context apparently means the interest is converted to principal. That is, interest is compounded monthly.
"Annuity immediate" means the payments are made at the beginning of the period, so do not earn interest for the period.
<95141404393>