Respuesta :
Answer: He should invest in second bank to get the most interest over the three year period.
Step-by-step explanation:
Here, the principal amount = $15000 and number of years=3
According to the question,
Compound Interest rate in first saving bank = 2.5% a year
Thus, the total amount by the first bank,
[tex]A_1 = 1500(1+\frac{2.5}{100})^3[/tex] = 16153.359375
Therefore compound interest by first bank,
[tex]I_1 = 16153.359375-15000=1153.359375[/tex]
While, Compound Interest rate in second saving bank = 3.8% for 1st year 1% extra for each extra year.
Thus, the total amount by the second bank,
[tex]A_2 = 1500(1+\frac{3.8}{100})(1+\frac{4.8}{100})(1+\frac{5.8}{100})[/tex] =17263.76688
Therefore compound interest by the second bank,
[tex]I_2 = 17263.76688-15000=2263.76688[/tex]
Since, [tex]I_2 >I_1[/tex]
Thus, he will get more interest in second bank than first bank.
Amount to be invested = 15000
Time period = 3 years
1st offer: Bank of Peace
Rate of interest or 'r'= 2.5% per year or 0.025
Time or 't' = 3 year (As Macro wants to invest for 3 years)
Compound interest formula is =
[tex]A=P(1+\frac{r}{n})^{t}[/tex]
Here A = 15000; r=0.025; t=3; n=1 (n is the number of times interest is compounded per year)
Putting all the values in the given formula we get
[tex]15000(1+\frac{0.025}{1})^{3}[/tex]
= 16153.36
Hence total interest earned = 16153.36-15000 = 1153.36
2nd offer: Bank of Trust
This bank is giving rate of interest as 3.8% for 1st year and 1% extra for each extra year.
Means 1st year rate = 3.8%
2nd year rate = 4.8%
3rd year rate = 5.8%
So putting the values of A = 15000; r=3.8 or 0.038 ; t=1 (the interest change changes after 1st year) and n=1 in the formula we get
For 1st year the amount becomes =
[tex]15000(1+\frac{0.038}{1})^{1}[/tex] = 15570
For next year the interest rate is 4.8% and P = 15570 and r=4.8% or 0.048 and t=1
Amount becomes = 16317.36
For third year the rate becomes 5.8% and P= 16317.36 t= 1 and n=1
So amount becomes = 17263.77
Hence total interest earned = 17263.77- 15000 = 2263.77
Hence, the Bank of trust is preferable for Macro as it gives a higher interest value.
