Question

1.

A friend asks to borrow $57 from you and in return will pay you $60 in one year. If your bank is offering a 6% interest rate on deposits and loans:

(a) How much (in $) would you have in one year if you deposited the $57 instead? (Round your answer to the nearest cent.)

(b) How much money (in $) could you borrow today if you pay the bank $60 in one year? (Round your answer to the nearest cent.)

(c) Should you loan the money to your friend or deposit it in the bank? (Consider the situation from a purely financial point of view.)

You should deposit the money in the bank or lend the money to your friend because it brings you more or less money at the end of the year.

1.2

Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $7,075.68 in it and pays a 9% interest rate.

(a) How much money (in $) would be in the account if you left the money there until your twenty-fifth birthday? What if you left the money until your sixty-fifth birthday? (Round your answers
to the nearest cent.)

twenty-fifth birthday:
sixty-fifth birthday:

(b) How much money (in $) did your grandfather originally put in the account? (Round your answer to the nearest cent.)

Answer 1

1.

1. Future value is calculated as P * (1+i)^t where p = Principal, i = interest rate and t = term. By using this formula, the answer is 57 * (1+0.06)^1 = $60.42. Thus, if I deposited $57 in the bank for one year, I would get $60.42.
2. Bank charges the interest of 6%. Hence the borrowed amount = FV / ((1+i)^t). By using this formula, the answer is 60 / (1+0.06)^1) = $56.60. Thus, I can borrow $56.60 today if I pay the bank $60 in one year.
3. If I lend $57 to my friend, I would get $60 back in in one year. However, if I deposit the same amount into the bank, I would get $60.42 as calculated in a). Thus my return is maximised when I deposit money into bank. Hence purely from financial standpoint, I should deposit money into bank. ​

​​​​​​2.

1. Current value (CV) = $7,075.68, Interest (i) = 9% p.a. Since I want to know the future value (FV) when I am 25^th year old, investment period (t) = 25 – 18 = 7 years. Hence FV can be calculated with the formula CV * (1+i)^t = 7,075.68 * (1+0.09)^7 = 12934.62. Thus, there would be $12,934.62 in the account if I left the money until my twenty-fifth birthday. Current value (CV) = $7,075.68, Interest (i) = 9% p.a. Since I want to know the future value (FV) when I am 65^th year old, investment period (t) = 65 – 18 = 47 years. Hence FV can be calculated with the formula CV * (1+i)^t = 7,075.68 * (1+0.09)^47 = 406268.91. Thus, there would be $406,268.91 in the account if I left the money until my sixty-fifth birthday
2. Let’s call the amount my grandfather originally put in the account as principal value (PV). Current value (CV) = $7,075.68, Interest (i) = 9% p.a. Period (t) = 18 years. PV can be calculated with the formula = CV / ((1+i)^t). Hence CV = 7075.68 / ((1+0.09)^18) = 1500. Thus, my grandfather originally put in $1,500 into the account.

Happy Learning!