Question

Lin wonders how much money she could save over 30 years if she puts $100 at the start of each year into an account with 3% interest per year compounded annually at the end of the year. She calculates the following, but thinks she must have done something wrong since that seems like a lot of money: 1-1.330

total amount = 100 1-1.3³⁰/1-1.3= 872,998.55
What did Lin forget in her calculation? How much should her total amount be?

Answer 1

Lin's 30-year savings miscalculation ignores interest earned each year. Her final sum is $243.80.

Lin is right to be suspicious of her calculation. She has forgotten to take into account the fact that she is making deposits at the beginning of each year, not at the end. This means that her money is earning interest for the entire year, not just for the last year.

To calculate the correct amount, we can use the formula for compound interest:

A = P(1 + r)^n

Where:

A is the final amount

P is the principal (the amount of money deposited each year)

r is the interest rate

n is the number of years

In this case, P = $100, r = 3%, and n = 30. Plugging these values into the formula, we get:

A = $100(1 + 0.03)^30

A = $100(1.03)^30

A = $100 * 2.438

A = $243.80

So, the total amount of money Lin will have after 30 years is $243.80.