Question

Alan Burnie has just started work and has been wanting to buy a sleek powerboat for sometime. Rather than purchase and finance now, he plans to save every three months and increase the deposits by 3% per annum as he expects raises at least that large. How much must the first deposit be if the boat costs $25,000 today and he expects to earn 10% on the money over the next five years?

Answer 1

You would like to save every 3 months or quarterly to accumulate amount to buy a boat

The deposits are subject to increase with evry payment at 396 per annum

Calculating the first deposit need to be made using Present value of Growing annuity formula:

PresentValue = C * 1-[(1+g)ⁿ (1+r)-ⁿ] / r - g

Where C = First Payment

r = Periodic Interest rate = 10%/4 = 2.5%

g= Growth rate = 3%/4 = 0.75%

n= no of periods = 5 years* 4 = 20

Present Value = $25,000

25, 000 = C * 1- [(1+0.0075)²⁰ * (1+0.025)^-20] / (0.025 – 0.0075)

25, 000 = C * 1 - [1.1611841423 * 0.61027094285] / (0.025 - 0.0075)

25, 000 = C * 16.6493176377

C = $1501.56

So, the first deposit should be $1501.56