Math question help

Question

Identify the Financial Application represented & the Desired Quantity in the problem.  

James and Susan wish to have $10,000 available for their wedding in 4 years. How much money should they set aside now at 6% compounded monthly in order to reach their financial goal?

Answer 1

A=P(1+r/n)^nt

where r= interest rate= .06

n= number of compounding periods per year =12 for monthly compounding

t= number of years= 4

P= starting amount, 10 for $10,000

A=ending amount 7.871 for $7,871

10 = P(1+.06/12)^12(4) = P(1.005^48)

P = 10/1.005^48= about 7.87098411

check by finding continuously compounded amount which should be slightly less

A=Pe^rt

A/10 = e^.06(4) = e^.24

ln(A/10) = .24

lnA-ln10 = .24

lnA = .24+ln10 = .24

$7,871 needed rounded off to nearest dollar

$7,870.98 rounded off to nearest cent

check the answer, use continuous compounding formula and see if it's slightly less

A=Pe^rt = 10= Pe^.24

ln(10/P) = .24

lnP = ln10-.24 = 2.0606

P = e^2.0606 = 7.86646

$7,866.46 is slightly less than $7,870.98

$4.52 less