Calculation of Savings and Compound Interest (Math Problem Sample)

Student’s Name
Instructor’s Name
Course Code/Number
Date
Calculation of Savings and Compound Interest
Task 1
To help Janette cover her college expense, parents provide Janette with a monthly allowance of $340. Besides, Janette earns $600 per month from the part-time job. Janette has to pay $200 in rent expense and $ 75 per month for her car insurance. Janette plans to spend monthly $80 on clothes, $50 for personal care, and $100 for entertainment. Janette also estimates her monthly eating out expense at $140, and she expects that $100 will be enough to cover all her other spending. Given that Janette follows the above income/spending schedule, how much can she put aside within eight months? Assume Janette puts the amount she put aside within eight months on the account that earns 4.75% per year, compounded annually. What would be the balance of this account in five years? Round your answers to the nearest dollar. Show your work.
Calculation of Janette’s savings
In this case, Janette receives $340 from her parents and an additional $600 from her part-time job. Therefore, Janette’s total monthly income is:
$340+ $600= $940
Out of her total income, Janette expects to spend $200 on rent, $75 on car insurance, $80 on clothes, $50 on personal care, $100 on entertainment, $140 on eat-outs, and $100 on other expenses every month. Her total monthly expenditure will be as shown below.
$200 + $75+ $80 + $50 + $100 + $140 + $100 = $745
Total monthly expenditure is $745.
Janette receives a total of $940 each month and spends $745. Therefore, her monthly savings will be:
$940- $745=$195
Monthly savings is $195; hence, in 8 months, she will save a total of:
$195 ×8=$1560
Therefore, if Janette follows the mentioned income/spending schedule, she will manage to put aside $1560 within eight months.
Calculation of Janette’s balance from her savings.
In this case, the savings will earn an interest of 4.75% per year. Since the interest earnings are compounded, we calculate the compound interest for the five years. The compound interest is calculated by multiplying every year’s new balance by the stated interest rate, as shown below.
The interest earnings formula (per year) is:I=PrT
Where:
* I is the interest earned
* P is the principal amount
* r is the interest rate in decimals – divided by 100%
* T is time or the period of savings (Cayabyab 1).
1 In the first year, Janette will earn an interest of:
$1560 × 4.75100 ×1=$74.1
Rounding $74.1 to the nearest dollar gives $74. With an interest of $74, Janette will have a total of $1634 in her account in the first year.
$1560 + $74= $1634
2 In the second year, Janette will earn an interest of:
$1634 × 4.75100 ×1=$77.615
Roundi