Respuesta :
Answer:
$367.86
Explanation:
To calculate this, we use the formula for calculating future value annuity (FVA) due as follows:
FV = M × {[(1 + r)^n - 1] ÷ r} × (1 + r) ................................. (1)
Where,
FV = Future value of an annuity or the cost of sailboat = $20,000
M = Amount of each annuity or to deposit monthly = ?
r = Monthly interest rate = 0.06 ÷ 12 = 0.005
n = number of months = 4 years × 12 = 48
Substituting the values into equation (1), we have:
20,000 = M × {[(1 + 0.005)^48 - 1] ÷ 0.005} × (1 + 0.005)
20,000 = M × 54.3683213801713
Making M the subject of the formula and solve, we have:
M = 20,000 ÷ 54.3683213801713 = $367.86
Therefore, Mr. Flores should deposit $367.86 in this account at the beginning of each month to be able to pay cash for the sailboat in 4 years.
The amount that needs to deposit into the account is $367.86
Calculation of the amount:
Since The sailboat i.e. interested in purchasing in 4 years that costs $20,000. An account at Invest Well Bank should earn 6% per year compounded monthly.
Now the monthly payment is
Future value = Monthly payment × {[(1 + rate of interest)^number of months - 1] ÷ rate of interest} × (1 + rate of interest)
Here future value = $20,000
Monthly rate of interest = 0.06 ÷ 12 = 0.005
Number of months = 4 years × 12 = 48
So, monthly payment is
Here M denotes the monthly payment
20,000 = M × {[(1 + 0.005)^48 - 1] ÷ 0.005} × (1 + 0.005)
20,000 = M × 54.3683213801713
M = 20,000 ÷ 54.3683213801713
= $367.86
Hence, we can conclude that The amount that needs to deposit into the account is $367.86
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