Milos wants to invest his savings in a bank for 5 years. He has £21000 to invest and receives offers from two banks.
Bank Venus:
2.1% per year
Compound interest
Bank Pacific:
4.9% for 1st year 1.5% for each extra year Compound interest
Which bank should Milos choose to get the most interest over the 5-year period? You must show all your working.
First, let's calculate how much each bank would offer at the end of 5 years:
Bank Venus:
Year 1: £21000 * 2.1% = £441 interest
Year 2: (£21000 + £441) * 2.1% = £462.63 interest
Year 3: (£21000 + £441 + £462.63) * 2.1% = £485.32 interest
Year 4: (£21000 + £441 + £462.63 + £485.32) * 2.1% = £509.16 interest
Year 5: (£21000 + £441 + £462.63 + £485.32 + £509.16) * 2.1% = £534.19 interest
Total interest from Bank Venus over 5 years: £2452.30
Bank Pacific:
Year 1: £21000 * 4.9% = £1029 interest
Year 2: (£21000 + £1029) * 1.5% = £347.85 interest
Year 3: (£21000 + £1029 + £347.85) * 1.5% = £360.32 interest
Year 4: (£21000 + £1029 + £347.85 + £360.32) * 1.5% = £373.34 interest
Year 5: (£21000 + £1029 + £347.85 + £360.32 + £373.34) * 1.5% = £386.93 interest
Total interest from Bank Pacific over 5 years: £2497.36
Therefore, Milos should choose Bank Pacific as it offers the most interest over the 5-year period.
To determine which bank will provide the most interest over the 5-year period, let's calculate the amount of interest earned from each bank.
For Bank Venus:
Principal (P) = £21,000
Annual Interest Rate (r) = 2.1% = 0.021
Time (t) = 5 years
Using the compound interest formula: A = P(1 + r/n)^(n*t)
where A is the future value, n is the number of compounding periods per year.
Bank Venus compounds the interest annually, so n = 1.
A = £21,000(1 + 0.021/1)^(1*5)
A = £21,000(1.021)^5
A = £21,000(1.1127)
A ≈ £23,364.7
Interest earned = A - P
Interest earned = £23,364.7 - £21,000
Interest earned ≈ £2,364.7
For Bank Pacific:
Principal (P) = £21,000
First-year Annual Interest Rate (r1) = 4.9% = 0.049
Remaining years Annual Interest Rate (r2) = 1.5% = 0.015
Time (t) = 5 years
Using the compound interest formula for each year:
Year 1:
A1 = P(1 + r1/n)^(n*t)
A1 = £21,000(1 + 0.049/1)^(1*1)
A1 = £21,000(1.049)
A1 ≈ £22,029
Remaining years (2-5):
A2-5 = A1(1 + r2/n)^(n*(t - 1))
A2-5 = £22,029(1 + 0.015/1)^(1*4)
A2-5 = £22,029(1.015)^4
A2-5 = £22,029(1.0609)
A2-5 ≈ £23,369.5
Total future value (A) = A1 + A2-5
A = £22,029 + £23,369.5
A ≈ £45,398.5
Interest earned = A - P
Interest earned = £45,398.5 - £21,000
Interest earned ≈ £24,398.5
Therefore, Bank Pacific would provide the most interest over the 5-year period, with approximately £24,398.5 earned, compared to Bank Venus' interest of approximately £2,364.7.