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To join an upscale country​ club, an individual must first purchase a membership bond for​ $20,000. In​ addition, monthly membership dues are​ $250. Suppose an individual wants to put aside a lump sum of money now to pay for her basic country club membership expenses​ (including the​ $20,000 bond) over the next 30 years. She can earn an APR of​ 6%, compounded​ monthly, on her investments. What amount must this person now commit to the​ membership?

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Answer: $61,697.90

Explanation:

GIVEN the following ;

Membership bond = $20,000

Monthly membership due= $250

Annual percentage rate(APR) = 6% = 0.06

monthly rate (r) = 0.06 ÷ 12 = 0.005

Payment per period(P) = $250

Using the formula for present value of ordinary annuity:

PRESENT VALUE (PV) =

P[(1 - ((1 + r)^(-n)) ÷ r]

$250 [ 1 - ((1 + 0.005)^-360))÷0.005]

$250 [( 1 - (1.005)^-360)÷ 0.005]

$250 × [0.83395807196 ÷ 0.005]

$250 × 166.791614392335

PV = $41,697.90

Membership bond + present value

$20,000 + $41,697.90

= $61,697.90

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