Answer:
(a) The amount needed is $192,000.
(b) The monthly payment is $150.98.
Step-by-step explanation:
Note: There are errors in this question. The correct question is therefore provided before answering the question as follows:
Susan and Bill Stamp want to set up a TDA that will generate sufficient interest at maturity to meet their living expenses, which they project to be $1,200 per month. (Round your answers to the nearest cent.)
(a) Find the amount needed at maturity to generate $1,200 per month interest, if they can get 7.25% interest compounded monthly.
(b) Find the monthly payment that they would have to make into an ordinary annuity to obtain the future value found in part (a) if their money earns 9.75% and the term is twenty years.
The explanation of the answer is now given as follows:
(a) Find the amount needed at maturity to generate $1,200 per month interest, if they can get 7.25% interest compounded monthly.
This can be calculated using the following future value formula:
FV = P / i ........................... (1)
Where;
FV = Amount needed at maturity = ?
P = Monthly payment or amount to generate monthly = $1,200
i = monthly interest rate = Annual interest rate / 12 = 7.25% / 12 = 0.075 / 12 = 0.00625
Substituting the values into equation (1), we have:
FV = $1,200 / 0.00625 = $192,000
Therefore, the amount needed is $192,000.
(b) Find the monthly payment that they would have to make into an ordinary annuity to obtain the future value found in part (a) if their money earns 9.75% and the term is twenty years.
This can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (2)
Where,
FV = Future value = $192,000
M = Monthly payment = ?
r = Monthly interest rate = 9.75% / 12 = 0.0975 / 12 = 0.008125
n = number of months = 25 years * Number of months in a year = 25 * 12 = 300
Substituting the values into equation (2) and solve for M, we have:
$192,000 = M * (((1 + 0.008125)^300 - 1) / 0.008125)
$192,000 = M * 1271.65920375075
M = $192,000 / 1271.65920375075
M = $150.98
Therefore, the monthly payment is $150.98.