You would like to buy a retirement home in Florence, Italy in 5 years. The type...

You would like to buy a retirement home in Florence, Italy in 5 years. The type of home you want to buy currently costs $538,108, but you expect the price to rise at 3% per year for the next 5 years.

If your investments earn 5.21% APR compounded annually (nominal), how much do you have to invest in years 1 to 5 to be able to purchase your retirement home?

Expert Solution

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Future value of home=538,108*(1.03)^5

=538,108*1.15927407

=$623814.651

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

623814.651=Annuity[(1.0521)^5-1]/0.0521

623814.651=Annuity*5.54885857

Annuity=623814.651/5.54885857

=$112422.16(Approx)

jeff jeffy answered 2 years ago

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