Answer:
1.93618 or 1.94 years
Step-by-step explanation:
Monthly household income = 1400(Since you are using just one spouse's income as savings)
Down payment Needed = 20% of $165,000 = $33,000
Interest rate = 7.83% compounded monthly.
This can be easily solved using a financial calculator by inputting following variables
N = this is what we have to calculate.
Interest rate = 7.83%/12 = 0.6525% -----> since it is compounded monthly.
Present Value = 0
PMT = -1400(This is what you intend to invest). Ensure that you put a negative sign here. Because "Cash out flow is treated as negative and cash inflow as positive)
Future Value = 33,000(The required down payment on the house)
When you solve for N, you get the answer as 23.23415 months. To get it in years, divide it by 12.
23.23415/12 = 1.93618 or 1.94 years
Alternatively, you can use the formula =NPER (0.6525%,-1400,0,33000,0) in Excel to obtain the number of months as 23.23415. 0.6525% is the monthly interest rate, -1400 is the payment per period, 0 is the Present Value, 33000 is the required down payment, and the last zero is telling excel to calculate everything at the end of the period