This paper solves questions on the Time Value of Money)
1. You would like to take a cruise in six years. The cruise currently costs $4,250. You expect the price to increase by 4% annually. You can earn 5% on your savings. How much do you need to save at the end of each month so you can afford your cruise in six years?
Current Cost of Cruise: $ 4,250
Price Increase Per Year: 4% or 0.04
Cost after 6 Years: 4250 x (1.04)6
= 4250 x 1.2563
= $ 5,339.27
Savings Rate = 5% = 0.05
The question as to how much would one need to save per month so that they can afford a cruise of $5,339.27 in 6 years is the same as asking: What amount of money per month would one have to invest @5% in order to save $ 5,339.27 in 6 years.
Since the saving occurs each month, there would be 6 x 12= 72 interest periods.
Answer is given by the formula: 5339.27 / PVIFA(1+.05/72)72
Tables for 72 interest periods were not available, so only the formula is given.
2. You invest $250 in your savings account at the end of each year and earn an average of 6% per year in interest. How much will you have in your savings account at the end of forty years?
Saving per year = $250
Rate of Interest = 6% or 0.06
Savings after 40 years = 250 FVIFA 0.06,40 = 250 x 154.76 = $38,690.
3. You want to have $40,000 to buy a new boat in six years. How much do you have to save at the end of each year to reach this goal if you earn 5% a year on your savings?
Sum Desired at end of 6 years = $40,000
Interest Earned Per Year = 5% or 0.05
How Much to Save each year = 40000 / PVIFA 0.05,6 = 40000 /5.0757 = $7.880.68...