Question

Marco wants to invest his savings in a bank for 3 years. He has ?15000 to invest and recieves offers from two banks: bank of peace= 2.5% a year compound interest or bank of trust= 3.8% for 1st year 1% extra for each extra year. Which bank should marco choose to get the most interest over the three year period? You must show all your working

Answer 1

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,

$A_1 = 1500(1+\frac{2.5}{100})^3$ = 16153.359375

Therefore compound interest by first bank,

$I_1 = 16153.359375-15000=1153.359375$

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,

$A_2 = 1500(1+\frac{3.8}{100})(1+\frac{4.8}{100})(1+\frac{5.8}{100})$ =17263.76688

Therefore compound interest by the second bank,

$I_2 = 17263.76688-15000=2263.76688$

Since,  $I_2 >I_1$

Thus, he will get more interest in second bank than first bank.

Answer 2

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 =

$A=P(1+\frac{r}{n})^{t}$

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

$15000(1+\frac{0.025}{1})^{3}$

= 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 =

$15000(1+\frac{0.038}{1})^{1}$ = 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.