Question

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. You and your new spouse each bring home $1400 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 7.83% 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.)

Answer 1

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