Question

1. John Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. John has recently come into an inheritance of $500,000. He estimates that the boat he wants will cost $400,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 10% (compounded annually) to buy the boat at retirement?
2. On January 15, 2010, Dolan Corp. adopted a plan to accumulate funds for environmental improvements beginning July 1, 2014, at an estimated cost of $5,000,000. Dolan plans to make four equal annual deposits in a fund that will earn interest at 8% compounded annually. The first deposit was made on July 1, 2010. Dolan should make four annual deposits of ?

Answer 1

1.Computation of amount of John Fillmore's inheritance must he invest at an annual rate of 10% (compounded annually) to buy the boat at retirement:

Interest rate (i) = 10%

Future Value required at year 4 = $400,000

Number of years (n) = 4

Required present value = FVn​​​​(1+i)-n

FVn​ = $400,000

(1+i)-n  = (1+0.1)-4

(1+0.1)-4  = 1/  (1+0.1)4

  (1+0.1)4 = 1.4641

1/1.4641 = 0.683

While substituting,

$400,000 * 0.683 = $273,200.

Therefore, John must invest $273,200 to buy the boat at his retirement.

2.Computation of the amount of four annual deposits Dolan should make:

Amount required = $5,000,000

Years (n) = 4

Interest rate (i) = 8%

It is given that the first deposit was made on July 1, 2010.

So, equal annual deposit made on year 0. We have to calculate deposit of year 1,2 and 3.

The periodic payment, R may be found from

R = PVA / PVIF(i,n)

R = $5,000,000 / PVIF ( 8%, 4)

Since first installment made in year 0 the present Value factor of year 0 is taken as 1.

PVIF for year 1,2 & 3 is 2.577

Therefore, PVIF (8%, 4) = 1+2.577

= 3.577

While substituting,

= $5,000,000/ 3.577
= $1,397,819 (rounded off)

Dolan should make four annual deposits of $1,397,819.