Question

1.) I decide to take a trip around the world. My budget, since I want to go in style and take my time is $100,000. Since I don't want to sell any assets at the present, I'm going to save up for it. How much will I need to save at the end of each year, for 10 years in order to pay for the trip? The annual effective interest rate is 8%.

2.) At 10% effective annual interest, what year end annual amount deposited each year for twenty years is equivalent to $45,000 today?

Answer 1

1. Future value = $ 100,000 , Interest rate r = 8% = 8/100 = 0.08 , Time t= 10 yrs

Amount value = Savings value per year * (1+r) ^t

or,100,000 = X(1.08)¹⁰ + X(1.08)⁹ + ....... + X (1.08)¹

or, 100,000 = X (1.08¹⁰ + 1.08⁹ +...... + 1.08¹)

or, 100,00 = X *15.6

or, X = 100,000/15.6 = $6410 approx.

2. $ 45,000 = X (1+10/100)²⁰ + X (1+10/100)¹⁹ +....... + X (1+10/100)¹

or, $ 45,000 = X (1.1²⁰ + 1.1¹⁹+.... + 1.1¹)

or, $45,000 = X * 63

or, X = $45000/63 = $714 (approx)