Question

You plan to deposit $29535 into a savings account that pays 4% compounded annually for 22 years. In year 10 you had to withdraw $1678 for an emergency. How much will you have in your account at the end of 22 years? Enter your answer as follows: 12345 Round your answer. Do not use a dollar sign ("$"), any commas("), or a decimal point(""

Answer 1

Let us first look at the formula of compound interest.

A= P(1+r/n)^nt

Where A is the future value of the investment/loan, including interest
P is the principal investment amount (the initial deposit or loan amount)
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per year
t is the number of years the money is invested or borrowed for.

Now since our question calls for compounding annually, the value of n will be 1.

Let us break this question in two parts: one, before withdrawing the money

Second, after withdrawing the money.

Now putting all the values in the given formula, we have the following illustration :

A = 29535(1+4/100)^9

Now why we have taken t as 9? It is because in the 10th year you are withdrawing 1678, for which you won't get interest in the 10th year. Thus firstly we will compound the interest for 9 years.

Therefore we get A= 42038 (rounding off the decimals)

Now in the 10th year you withdraw 1678. So your remaining balance is 42038 - 1678 = 40360

Now for the remaining 13 years your principle amount is 40360.

Applying the formula once again:

A= 40360(1+4/100)^13

= 67202 (rounding of the decimals)

So you will receive 67202 after 22 years.

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