Question

A) How much money will be in your savings account on January 1, 2023 if you deposit $5,000 on January 1, 2020 and you earn 3.1% per year in interest? Interest is compounded annually on December 31

B) How much money would you have to deposit on January 1, 2020 to have $5,000 in your bank account on January 1, 2027 if the savings account paid 1.25% interest, compounded annually on December 31 of each year?

C) Suppose your discount rate is 0.1% per week and you get paid $1,000 per week at the end of each week. What is the total value you place on all of your paychecks for the upcoming year, if it is the first day of the year?

Answer 1

A.

T = 2023 - 2020 = 3

I = 3.1%

F = P *(1+I)^t

F = 5000 * (1+0.031)^3 = 5000 * 1.031 ^ 3 = 5479.56

B.

T = 2027 - 2020 = 7

I = 1.25%

P = F / (1+I)^t

P = 5000 / (1+0.0125)^7 = 5000 / (1.0125)^7 = 4583.58

C.

Total weeks in one year = 52

I = 0.1%

A = 1000

P = 1000 * (P/A, 0.1%,52) = 1000 * 50.646467 = 50646.47