Question

Hei has $1800 in a retirement account earning 3% interest compounded annually . Each year after the first she makes an additional deposit of $1800. After 5 years what was her account balance if she did not make any withdrawals? Round each year's interest to the nearest cent if necessary

Answer 1

The amount that will be in her account after five years if she doesn't make any withdrawal before then is $11,643.14

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) =

`C[((1+i)^(n)-1 )/(i)]`

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:-

`1800[((1+0.03)^(6)-1)/(0.03)]`

`1800[(1.03^(6)-1)/(0.03)]`

`1800[(1.194052296529-1)/(0.03)]`

`1800[(0.194052296529)/(0.03)]`

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

Answer 2

$11643.14

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.