Question

Diego wonders how much money he could save over 25 years if he puts $150 a year into an account with 4% interest per year compounded annually. He calculates the following, but thinks he must have something wrong, since he ended up with a very small amount of money: What did Diego forget in his calculation? How much should his total amount be? Explain or show your reasoning.

Answer 1

Answer: When you deposit money into a savings account, the bank pays you a fee for the use of

your money. This fee is called interest and is determined by the amount deposited, the

duration of the deposit, and the interest rate. The amount deposited is called the principal or present value, and the amount to which the principal grows (after the addition

of interest) is called the future value or balance.

The entries in a hypothetical bank statement are shown in Table 1. Note the following facts about this statement:

1. The principal is$100.00$. The future value after 1 year is $104.06$.

2. Interest is being paid four times per year (or, in financial language, quarterly).

3. Each quarter, the amount of the interest is 1% of the previous balance. That is,$1.00$

is 1% of$100.00, 1.01 is 1% of 101.00$, and so on. Since 4 * 1% is 4%, we say that

the money is earning 4% annual interest compounded quarterly.

Step-by-step explanation:

STEP:1 (a) The annual interest rate is 3%, and the number of interest periods is 2. Therefore,

i = 3%

2 = .03

2 = .015.

(b) The annual interest rate is 2.4%, and the number of interest periods is 12. Therefore,

i = 2.4%

12 = .024

12 = .002. Now

Consider a savings account in which the interest rate per period is i. Then the interest earned during a period is i times the previous balance. That is, at the end of an interest period, the new balance, Bnew, is computed by adding this interest to the previous

balance, Bprevious. Therefore,

$Bnew = 1 # Bprevious + i # BpreviousBnew = (1 + i) # Bprevious. ($

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