Pertanyaan:
Case 2- Planning: The Key to Wealth
Abdol Akhim has just come from a Personal Finance class where he learned that he can determine how much his savings will be worth in the future. Abdol is completing his two-year business administration degree this semester and has been repairing computers in his spare time to pay for his tuition and books.
Abdol got out his savings records and decided to apply what he had learned. He has a balance of $1,000 in a money market account at First Savings Bank, and he considers this to be an emergency fund. His instructor says that he should have 3–6 months of his total bills in an emergency fund. His bills are currently $700 a month. He also has a checking account and a regular savings account at First Savings Bank, and he will shift some of his funds from those accounts into the emergency fund. One of Abdol’s future goals is to buy a house. He wants to start another account to save the $8,000 he needs for a down payment.
- How much interest will Abdol receive on $1,000 in a 365-day year if he keeps it in the money market account earning 2.25% compounded daily?
- How much money must Abdol shift from his other accounts to his emergency fund to have four times his monthly bills in the account by the end of the year?
Abdol realizes he needs to earn more interest than his current money market can provide. Using annual compounding on an account that pays 5.5% interest annually, find the amount Abdol needs to invest to have the $8,000 down payment for his house in 5 years.
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Bukti:
Given: money market rate 2.25% compounded daily, r=0.0225r=0.0225, n=365n=365. Monthly bills = $700 → emergency target = 4×700=$2,800.4\times700=\$2{,}800.
1) Interest on $1,000 after 365 days (2.25% compounded daily)
Amount after 365 days:
A=1000(1+0.0225365)365=1000⋅(1+0.0225/365)365A = 1000\left(1+\dfrac{0.0225}{365}\right)^{365}=1000\cdot(1+0.0225/365)^{365}
Computed:
A≈$1,022.75A \approx \$1{,}022.75
Interest earned ≈ $22.75.
2) How much to shift from other accounts to reach 4× monthly bills ($2,800) by end of year
Two reasonable interpretations — I give both and label the assumption:
A — Transfer now (so the transferred money also earns the same daily compounding).
Let SS = amount shifted now. Then final balance = (1000+S)⋅(1+0.0225/365)365=2800(1000+S)\cdot(1+0.0225/365)^{365}=2800.
Solving gives S≈$1,737.71S \approx \$1{,}737.71.
Answer (transfer now): $1,737.71.
B — Transfer at the end of the year (shifted money does not earn interest in the money market during the year).
Then you need: 1000⋅(1+0.0225/365)365+S=28001000\cdot(1+0.0225/365)^{365} + S = 2800.
Using the amount from (1), this gives S≈$1,777.25S \approx \$1{,}777.25.
Answer (transfer at year-end): $1,777.25.
(Which to use depends on whether Abdol moves the money now — if he does, use the first number.)
3) Amount to invest now at 5.5% compounded annually to reach $8,000 in 5 years
Use annual compounding:
P(1+0.055)5=8000⇒P=8000(1.055)5P(1+0.055)^5 = 8000 \quad\Rightarrow\quad P=\dfrac{8000}{(1.055)^5}
Computed:
P≈$6,121.07P \approx \$6{,}121.07