Ben is saving to go on a South Pacific cruise four years from today. The trip wi

Question

Ben is saving to go on a South Pacific cruise four years from today. The trip will cost $10,000.  To fund the trip he has decided to put his annual bonus into an account that will earn 6% interest compounded annually.  According to his calculations his first bonus (to be received at the end of the year) will be $1,000. His second bonus (to be received 2 years from today) will be $2,000 and his third bonus (3 years from today) will be $3,000.  

a) How much will Ben have saved by the end of year 4?

b) How much will he need to deposit TODAY in order to have enough for the trip?

Explanation / Answer

Part-A

Let the amount saved at the end of 4th year be x

1000*(1.06)^3 + 2000*(1.06)^2 + 3000*(1.06)^1 + x = 10000

1191.016+2247.2+3180+ x = 10000

X = 3381.78

Part-B

b) How much will he need to deposit TODAY in order to have enough for the trip?

Let the amount to be deposited today be x

X(1.06)^4 = 10000

X = 10000/(1.06^4)

X= 7920.94

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