1. Savings Goals: Suppose that you are considering buying a 3D printer. You plan

Question

1. Savings Goals: Suppose that you are considering buying a 3D printer. You plan on saving every week for a year in a savings account paying a nominal interest rate of 6% per year. Currently, the printer costs $1,000, and you expect the real cost to be unchanged when you go to buy it. Finally, you believe that the inflation rate in the economy will be 2% over the next year. (a) How much, in nominal dollars, do you expect the printer to cost at the end of the year? (b) What is the nominal interest rate expressed weekly? (c) How many nominal dollars would you need to save each week in order to reach your savings goal in one year? (d) Suppose that instead of saving the money in a bank account, you instead saved it by putting it in a jar in your house. Ignoring the possible risk of theft, how many nominal dollars would you need to save each week to hit your goal of $1,000? (e) Comment on the difference between your answers to part (c) and (d). Is the difference large? Why or why not?

Explanation / Answer

a. Cost of Printer at the end of the Year = 1,000 x 1.02 = $1,020

b. Nominal Interest Rate expressed weekly = 6 / 52 = 0.115%

c. Formula to calculate Future Value of Annuity = P / i [(1 + i)^n - 1]

FV = Future Value = 1,000 P = Payment every week, i = Interest = 6%, n = Number of Years= 1

1,000 = X /0.06 / 52 [ (1 + 0.06)^1x52 - 1]

P = 18.67

So, we require to save $18.67 per week.

d. Dollar require to save each week = 1,000 / 52 = $19.23

e. The per week difference is not large but if we look for the whole year then the difference is around $30 which is a large sum.

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