Question

jimmy identified his ‘dream’ retirement home at the end of 2010. The property is currently (end 2010) valued at $850,000 and is likely to appreciate in value over the next 15 years (his anticipated retirement date from now) as follows:
-Years 1 to 5 by 8% p.a.,
-Years 6 to 10 by 10% p.a.,
and -Years 11 to 15 by 15% p.a.
he can earn a net 14% p.a. rate of return on any investment funds he puts aside to pay for his ‘dream’ retirement home over the 15 year term. Moreover, as a result of an inheritance from his grandfather, he also anticipates that he will be able to add a lump sum of $300,000 to these investment funds (used to pay for his retirement home) in 3 years from now.

a)Given the information provided above, approximately what amount must Jack invest on an annual basis in order to be able to buy his dream home at retirement?
i)At the end of each of the next 15 years?
ii)At the beginning of each of the next 15 years?  

Answer 1

Answer:

Current value of property ( End 2010) = $850,000

Future Value Interest Factors for One Dollar Compounded at 8% for 5 Periods = 1.46933

Future Value Interest Factors for One Dollar Compounded at 10% for 5 Periods = 1.61051

Future Value Interest Factors for One Dollar Compounded at 15% for 5 Periods = 2.011357

As value of property at the end 5 year (End 2015) = $850,000 * 1.46933

As value of property at the end 10 year (End 2020) = $850,000 * 1.46933 * 1.61051

As value of property at the end 10 year (End 2025) = $850,000 * 1.46933 * 1.61051 * 2.011357 = $4,045,669

To pay for same:

Jack will get lump sum of $300,000 from inheritance 3 years from now (End 2013) which he can invest for 12 years at 14% p.a.

Future Value Interest Factors for One Dollar Compounded at 14% for 12 Periods = 4.817905

Hence Future value of $300,000 after twelve years (at the end of 2025) =$300,000 * 4.817905 = $1,445,371

Now balance required to be funded at the of 2025 = $4,045,669 - $1,445,371 = $2,600,297

As such Jimmy need to save an annual amount and earn at the rate of 14% p.a. so that he gets at the end of 15 years from now an amount = $2,600,297

Answer i):

Let us assume he saves amount = X at the end of each year for 15 years

Future Value Interest Factors for a One-Dollar Annuity Compounded at 14% for 15 Periods = 43.842

Hence,

X * 43.842 = $2,600,297

=> X = $59,310

Hence Jack needs to invest approximately $59,310 each year at the end of each of the next 15 years

Answer ii)

Let us assume Jack invests $Y at the beginning of each year for 15 years.

Future value Interest Factors for a One-Dollar Annuity (in advance) Compouned at 14% for 15 Periods = 49.980

Hence,

Y * 49.980 = $2,600,297

=> Y = $2,600,297 / 49.980 = $52,026

Hence Jack needs to invest approximately $52,026 each year at the beginning of each of the next 15 years