You and your new spouse each bring home $1600 each month after taxes and other payroll deductions. By living frugally, you intend to live on just one paycheck and save the other in a mutual fund yielding 7.85% compounded monthly. How long will it take to have enough for a 20% down payment on a $165,000 condo in the city? (Round your answer to two decimal places.)

 

It will take them 19.41 months to have enough for the 20% down payment on a $165,000 condo in the city.

You and your new spouse each bring home $1600 each month after taxes and other payroll deductions. By living frugally, you intend to live on just one paycheck and save the other in a mutual fund yielding 7.85% compounded monthly. How long will it take to have enough for a 20% down payment on a $165,000 condo in the city? (Round your answer to two decimal places.)

Step 1: Calculate the down payment

Down payment= Price of the condo * Down payment rate

Price of the condo= $165,000

Down payment rate= 20% or 0.2

Down payment= $33,000

Step 2: Calculate the number of months

FV= P((1+r)ⁿ-1)/r

FV is the future value (down payment)= $33,000

P is the monthly savings= $1,600

r is the interest rate= 7.85%; make it monthly (7.85%/12)= 0.654167 or 0.00654167

n is the number of months= ?

$33,000= $1,600((1+0.00654167)ⁿ-1)/0.00654167

$33,000= $1,600(1.00654167ⁿ-1)/0.00654167

$33,000/$1,600=(1.00654167ⁿ-1)/0.00654167

20.625=(1.00654167ⁿ-1)/0.00654167

20.625 * 0.00654167=(1.00654167ⁿ-1)

0.134922=1.00654167ⁿ-1

1.134922=1.00654167ⁿ

1.00654167ⁿ= 1.134922

Introduce logarithms:

nLog 1.00654167= Log 1.134922

n= Log 1.134922/Log 1.00654167

n= 19.410555

n≈ 19.41

Therefore, it will take them 19.41 months to have enough for the 20% down payment on a $165,000 condo in the city.