Question

You are trying to save up to take a trip around the world in four years from today (t=4) which will cost $40,000. You currently have $25,000 in your bank account today (t=0). In addition, you plan on working for one year at which time you will deposit your savings from working into the bank account. If the interest rate is 4% p.a., how much savings from work do you need to deposit one year from today (t=1) in order to pay for your trip? How to calculate using financial calculator functions

Answer 1

Amount required for round trip after n = 4 years is $40000

Amount available today = PV = $25000

Let amount deposited after 1 year = P (this will grow for 3 years)

Interest Rate = r = 4% or 0.04

Value of an Investment X after n years at rate of interest r = X(1+r)ⁿ

Hence, Value of Investment at (t = 4 ) = PV(1+r)⁴ + P(1+r)³ = 25000(1+0.04)⁴ + P(1+0.04)³

This value should be equal to the amount required = 40000

=> 25000(1+0.04)⁴ + P(1+0.04)³ = 40000

=> 29246.464 + 1.125P = 40000

=> P = 9558.70

Hence, $9558.70 should be deposited at t = 1 to accumulate the required sum for the trip