1) If a young couple have already saved $10,000 for the purpose of buying a home and hope to have a total of $50,000 for the required down payment and closing costs for the future home they hope to buy, how much per month do they have to save and invest to reach this goal in 4 years from today, if an average annual rate of return of 6 % can be earned

Monthly deposit = $690.88

Explanation:

Giving the following information:

Lump sum = $10,000

Future value = $50,000

Number of years = 4 years

Interest rate = 6%

First, we need to calculate the final value of the first $10,000 investment.

FV = PV * (1+i) ^n

FV = 10,000 * (1.06) ^4 = $12,624.77

Investment needed = 50,000 - 12,624.77 = $37,375.23

Now, using the following formula we can determine the monthly deposit necessary:

FV = {A*[ (1+i) ^n-1]}/i

A = monthly deposit

Isolating A:

A = (FV*i) / {[ (1+i) ^n]-1}

i = 0.06/12 = 0.005

n = 12*4 = 48

A = (37,375.23*0.005) / [ (1.005^48) - 1]

A = $690.88