Question

A) Assume that you wish to make annual deposits into a savings account. The interest rate offered by the bank is 11%, and you plan to save for the next 12 years. If your goal is for the present value of your savings to be equal to $4,058, how much money must you deposit every year?

B) Assume you've just received a bonus at work of $3,812. You deposit that money in the bank today, where it will earn interest at a rate of 7% per year. How much money will you have in the account after 5 years?

C) Assume one year the basket of goods has a price level of $105, and the following year that same basket of goods is priced at $106. What was the rate of inflation over that year?

Answer 1

A)

Interest rate (r) = 11% or 0.11

No. of years (n) = 12 years

Present value = $4058

Solution :-

Annual deposits = (present value x r) [1 - (1 + r)^-n]

= ($4058 x 0.11) [1 - (1 + 0.11)^-12]

= $446.38 [1 - (1.11)^-12]

= $446.38 [1 - 0.28584082]

= $446.38 0.71415918

= $625.04

So. you must deposit $625.04 every year.

B)

Given,

Deposit = $3812

Interest rate (r) = 7% or 0.07

No. of years (n) = 5 years

Solution :-

Future value = deposit x (1 + r)ⁿ

= $3812 x (1 + 0.07)⁵

= $3812 x (1.07)⁵

= $3812 x 1.40255173 = $5346.53

So, you will have $5346.53 after 5 years.

C)

Current price = $105

Price next year = $106

Solution :-

Inflation rate = (Price next year - current price) current price

= ($106 - $105) $105

= $1 $105 = 0.0095 or 0.95%