Suppose an individual makes an initial investment of $1100 in an account that earns 7.3%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0).
(a) How much is in the account after the last deposit is made?
(b) How much was deposited?
(c) What is the amount of each withdrawal?
(d) What is the total amount withdrawn?
I don't know how to start this problem
To solve this question, we can break it down into four parts:
(a) How much is in the account after the last deposit is made?
To determine the amount in the account after 12 years, we need to calculate the compound interest on the initial investment and the monthly contributions. We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the initial investment (P) is $1100, the annual interest rate (r) is 7.3% or 0.073, the interest is compounded monthly (n = 12), and the time period (t) is 12 years.
Plugging these values into the formula, we get:
A = 1100(1 + 0.073/12)^(12*12)
Using a calculator, we can calculate the value of A, which is approximately $2751.82.
Therefore, the amount in the account after the last deposit is $2751.82.
(b) How much was deposited?
To calculate the total amount deposited, we need to multiply the monthly contribution amount ($100) by the number of months (12 years or 12 * 12 months).
Total deposited = $100 * (12 * 12)
Using a calculator, we find that the total amount deposited is $14,400.
Therefore, the total amount deposited is $14,400.
(c) What is the amount of each withdrawal?
To find the amount of each withdrawal, we divide the remaining balance in the account ($2751.82) by the number of months in the withdrawal period (5 years or 5 * 12 months).
Amount of each withdrawal = $2751.82 / (5 * 12)
Using a calculator, we get that the amount of each withdrawal is approximately $45.86.
Therefore, the amount of each withdrawal is approximately $45.86.
(d) What is the total amount withdrawn?
To calculate the total amount withdrawn, we multiply the amount of each withdrawal ($45.86) by the total number of withdrawals (5 years or 5 * 12 months).
Total amount withdrawn = $45.86 * (5 * 12)
Using a calculator, we find that the total amount withdrawn is $2,751.60.
Therefore, the total amount withdrawn is $2,751.60.