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.
Status: 100% Tercapai
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Bukti:
1. Bunga yang diterima pada $1.000 di money market (2,25% per tahun, dikompaun harian; 365 hari)
Rumus compounding harian:
FV= PV (1+r/365) ^365
Dimana PV = 1000, r = 0.0225
Perhitungan:
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suku bunga harian = 0.0225/365
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FV≈1000 × (1+0.0225/365)^365 ≈ 1,022.75
Bunga yang diterima = FV − PV ≈ $1,022.75 − $1,000 = $22.75
Jawaban: Abdol menerima sekitar $22,75 bunga selama 1 tahun; saldo akhir ≈ $1.022,75.
2. Berapa yang harus dipindahkan dari rekening lain agar dana darurat setara empat kali tagihan bulanan di akhir tahun?
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Target dana darurat = tagihan bulanan = 4 × $700 = $2.800
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Saldo awal di money market ($1.000) akan tumbuh menjadi ≈ $1.022,75 (lihat nomor 1).
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Jadi tambahan yang perlu dipindahkan dari rekening lain agar mencapai $2.800 pada akhir tahun:
Jumlah dipindah= 2,800 − 1,022.75 ≈ $1,777.25.
Jawaban: Abdol harus memindahkan sekitar $1.777,25 dari rekening lain ke money market agar pada akhir tahun memiliki empat kali tagihan bulanan ($2.800).
3. Berapa yang harus diinvestasikan sekarang agar punya $8.000 dalam 5 tahun pada suku 5,5% per tahun (compounded annually)?
Rumus nilai sekarang (PV) untuk mendapatkan FV setelah n tahun:
PV = FV/(1+r)^n
Dengan FV=8,000, r=0.055, .
Perhitungan:
PV≈8,000/(1+0.055)^5≈$6,121.07.
Jawaban: Abdol perlu menginvestasikan sekitar $6.121,07 sekarang pada rekening yang membayar 5,5% per tahun (dikonpaun tahunan) agar menjadi $8.000 dalam 5 tahun.