Question

In 10 years you are planning to buy a beach condo. The condo you want currently costs $100,000 and is expected to increase in value each year at a rate of 2.5 percent. If you can earn 10% annually on your investments, how much must you invest at the end of each of the next 10 years to be able to buy the condo?

Answer 1

8,031.94

Step-by-step explanation:

this problem can be solved first calculating the future value of the condo, so we can use the next formula:

`FV=PV*(1+i)^(n)`

where FV is future value, PV is the present value, i is the periodic interest rate and n is the number of periods. So applying to this particular problem we have:

`FV=100,000*(1+0.025)^(10)`

`FV=128,008`

now we must apply the concept of annuity, keep in mind that an annuity is a formula which allows you to calculate the future value of future payments affected by an interest rate.by definition the future value of an annuity is given by:

`s_(n) =P*((1+i)^(n)-1 )/(i)`

where
`s_(n)` is the future value of the annuity,
`i` is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so:

`128,008 =P*((1+0.1)^(10)-1 )/(0.1)`

Solving P we have:

P=8,031.94