Question

The Flores Family loves to go sailing on the weekends. Mr. Flores has decided to purchase a more spacious sailboat. The sailboat he is interested in buying in 4 years will cost him $20,000. An account at Invest Well Bank earns 6% per year compounded monthly. How much should Mr. Flores deposit in this account at the beginning of each month to be able to pay cash for the sailboat in 4 years?

Answer 1

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.