Question

Alan Burnie has just started work and has been wanting to buy a sleek powerboat for some time. 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?

A)$2,359.82 B)$1,561.49 C) $1,501.56 D) $2,081.99 E) $6,097.27

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 3% per annum

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

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

C = $1501.56

So, the first deposit should be $1501.56

option C

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