Answer:
$11643.14
Step-by-step explanation:
Hei started with $1800 in her account, which compounded annually at an interest rate of 3%. This means that her principal is $1800
She makes a yearly deposit of $1800 over 5 years
We calculated her accrued balance over the 5 years, we use the formula: I = P × R / 100 for each year.
Where P= principal, R= rate, I= Interest
Year 1 = 1800 × 3 / 100 = 54
Interest= $54
New principal will be 1800 + 54 + 1800 (annual additional deposit) = $3654
Year 2= 3654 × 3 / 100 = 109.62
Interest= $109.62
New principal will be 3654 + 109.62 + 1800 (annual additional deposit) = $5563.62
Year 3= 5563.62 × 3 / 100 = 166.91
Interest= $166.91
New principal will be 5563.62 + 166.91 + 1800 (annual additional deposit) = $7530.53
Year 4= 7530.53 × 3 / 100 = 225.92
Interest= $225.92
New principal will be 7530.53 + 225.92 + 1800 (annual additional deposit) = $9556.45
Year 5= 9556.45 × 3 / 100 = 286.69
Interest= $286.69
Total amount in her account will be 9556.45 + 286.69 + 1800 (annual additional deposit) = $11643.14
If Hei does not make any withdrawal within the 5 years, her account balance will be $11643.14 i.e. an accumulation of $10800 total deposit and $843.14 total interest.
Answer:
The amount that will be in her account after five years if she doesn't make any withdrawal before then is $11,643.14
Step-by-step explanation:
Extracting the key information from the question:-
***Hei has $1800 in a retirement account.
*** She earns 3% interest compounded annually.
*** After the end of each year, she makes extra deposit of $1800.
*** We are required to calculate the amount that would be in her account after five years if she doesn't make any withdrawal.
Since Hei had $1800 in that retirement account initially and earns 3% interest compounded annually, if she makes additional deposit of $1800 yearly for 5 years, then we can calculate the future value of her money using the annuity formula.
An annuity is a series of regular payments made that equal periods/intervals. Examples of annuities are monthly home mortgage payment, regular pension payments and deposits to an account.
The formula is:
Fv (ordinary annuity) =
[tex]C[\frac{(1+i)^{n}-1 }{i}][/tex]
Fv = future value
C = cash flow
i = interest rate
n = number of payments
In this case:
C = $1,800 (regular deposits)
i = 3% = 0.03 (interest rate)
n = 6 times (5 more payments plus the initial balance).
substituting appropriately:-
[tex]1800[\frac{(1+0.03)^{6}-1}{0.03}][/tex]
[tex]1800[\frac{1.03^{6}-1}{0.03}][/tex]
[tex]1800[\frac{1.194052296529-1}{0.03}][/tex]
[tex]1800[\frac{0.194052296529}{0.03}][/tex]
1800 × 6.4684098843
11,643.138
$11,643.14
Therefore, the amount that Hei's money will grow to after five years is $11,643.14
