Question

Mark needs $26,700 to purchase a boat. How much money will he need to invest today in a savings account earning 4.6% interest, compounding quarterly, to have enough money to purchase the boat in 12 years? (2 points)
$3,083.12

$15,422.28

$22,220.50

$25,266.90
The correct answer is $15,422.28, I just need the work to solve it. Can anyone help me please?

Answer 1

Answer:

• $15422.28

Step-by-step explanation:

• Future value FV = $26700
• Interest rate r = 4.6% = 0.046 per annum compounded
• Compound number n = 4 per year
• Time t = 12 years
• Initial amount P = ?

Use formula for future value, solve for P:

• FV = P*(1 + r/n)^(nt)
• 26700 = P(1 + 0.046/4)^(12*4)
• P = 26700 / 1.0115^48
• P = 15422.28