Marco wants to invest his savings in a bank for 3 years. He has borrowed £15,0000 to invest and receives offers from two banks. Bank 1 is: - 2.5 % per year compound interest and Bank 2 is: - 3.8% for 1st year and 1% for each extra year compound interest. Which bank should Marco choose to get the most interest over the 3 year period?

Marco should choose the first bank to get the most interest over 3 years (£1153.36)

Step-by-step explanation:

According to the question, Marco is trying to invest his savings of £15,000 in a bank for three (3) years.

Two banks presented an offer with different interest rates. Bank 1 offers 2.5% interes rate per year while Bank 2 offers 3.8% interest rate for the 1st year and 1% interest rate for subsequent years.

In order to calculate the interest amount offered by both banks, we use the formula:

I = P * R * T : 100

Where P = Principal amount to be invested

R = interest rate

T = Time in years

I = Interest amount

We will calculate the interest amount for each year, hence, T is 1 for each year.

Bank 1:

For 1st year;

P = £15,000, R = 2.5%, T=1

I = 15000 * 2.5 * 1 : 100

I = 375

To get the principal amount for year 2, we add 15000 + 375 = 15375

2nd year;

P = £15,375, R = 2.5%, T=1

I = 15375 * 2.5 * 1 : 100

I = 384.375

Principal amount for year3 = 15375 + 384.375 = 15759.38

3rd year;

P = £15,759.38, R = 2.5%, T=1

I = 15759.38 * 2.5 * 1 : 100

I = 393.98

Amount for three years = 15759.38 + 393.98 = £16153.36

Hence, for the first bank, a total amount of £16153.36 was realized after three years with a total interest amount of £16153.36 - £15000 = £1153.36

Bank 2:

For 1st year;

P = £15,000, R = 3.8%, T=1

I = 15000 * 3.8 * 1 : 100

I = 570

To get the principal amount for year 2, we add 15000 + 570 = 15570

N. B: The interest rate has been reduced for following years

2nd year;

P = £15,570, R = 1%, T=1

I = 15570 * 1 * 1 : 100

I = 155.7

Principal amount for year3 = 15570 + 155.7 = 15725.7

3rd year;

P = £15,725.7, R = 1%, T=1

I = 15725.7 * 1 * 1 : 100

I = 157.257

Amount for three years = 15725.7 + 157.257 = £15882.95

Hence, for the second bank, a total amount of £15,882.95 was realized after three years with a total interest amount of £15882.95 - £15000 = £882.95

The interest amount of Bank 1 (£1153.36) after three years of investing £15000 will be more than the interest amount (£882.95) of Bank2 after investing the same amount for 3 years. Hence, Marco should choose Bank 1 to invest his savings.

Marcos Should invest with the first bank

Step-by-step explanation:

Formula for finding compound interest is: A = p (1+/frac{r}{n}) ^{nt}

where

A = the future value of the investment

P = the principal investment amount (the initial deposit)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested

If marcos choose to invest with the first bank

A = 15000 (1+/frac{0.025}{12}) ^{12*3} = £16166.81

If he choose to invest with the second bank

His principal become 15570 in the first year because of the 3.8% offer from the bank and t becomes 2.

A = 15570 (1+/frac{0.01}{12}) ^{12*2} = £15884.27

Comparing the future value of his investment from both bank, Marcos will get more interest from investing with the first bank.