Natasha plans to deposit $4,000 per year in her account for each of the next 4
years. Thereafter, she expects to deposit $1,500 per year for another 4 years. All
deposits are made at year-end. Interest rates are expected to be 8 percent for the
next 2 years, and 11 percent thereafter. Interest is compounded annually. (a) What
will Natasha's bank balance be at the end of year 8?
first 4 years
S = 4000 [ 1.08^4 -1 ]/.08
= 18024.45
second 4 years
first what happens to the 18024.45 that we have in the account. It earns 11% compounded yearly
18024.45 (1.11)^4 = 27362.38
In addition we have 1500 per year deposited
S = 1500 [1.11^4 -1 ]/.11
= 7064.60
27362.38 + 7064.60 = 34426.98
Youre wrong you suck
To calculate Natasha's bank balance at the end of year 8, we need to calculate the future value of each set of cash flows and add them together.
Let's break down the problem:
1. Calculate the future value of $4,000 per year for each of the next 4 years.
- Using the formula for the future value of an ordinary annuity:
FV = P * (1 + r) ^ n
where FV is the future value, P is the annual deposit, r is the interest rate, and n is the number of years.
Plugging in the values:
FV1 = $4,000 * (1 + 0.08) ^ 4
= $4,000 * 1.3605
= $5,442
2. Calculate the future value of $1,500 per year for another 4 years.
- Using the same formula:
FV = $1,500 * (1 + 0.11) ^ 4
= $1,500 * 1.4641
= $2,196.15
3. Add the two future values together to get the total bank balance at the end of year 8:
Bank balance at year 8 = FV1 + FV2
= $5,442 + $2,196.15
= $7,638.15
Therefore, Natasha's bank balance at the end of year 8 will be $7,638.15.