Did I solve correctly? I don't know any other way to solve the question.
The cost of utilities, taxes and maintenance on a home is $3,000 per year. Calculate the amount of money
that would have to be invested now at 8% annual interest rate to cover these expenses for the next 5 years.
3,000*((((1+.08)^5)-1)/.08)=17,599.80
To calculate the amount of money that would have to be invested now at an 8% annual interest rate to cover these expenses for the next 5 years, you can use the formula for the present value of an annuity.
The formula is:
PV = PMT * (((1 + r)^n) - 1) / r
Where:
PV is the present value
PMT is the payment amount per period
r is the interest rate per period
n is the number of periods
In this case, PMT is $3,000 per year, r is 8% (or 0.08), and n is 5 years.
Plugging in the values into the formula, we get:
PV = 3,000 * (((1 + 0.08)^5) - 1) / 0.08
Simplifying further:
PV = 3,000 * (((1.08)^5) - 1) / 0.08
Calculating the value inside the parenthesis:
PV = 3,000 * (1.4693280896 - 1) / 0.08
Subtracting 1 inside the parenthesis:
PV = 3,000 * (0.4693280896) / 0.08
Calculating the final value:
PV = 17,599.80
So, the correct amount of money that would have to be invested now at an 8% annual interest rate to cover these expenses for the next 5 years is $17,599.80.
Yes, your calculation is correct.