Answer:
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.
Answer:
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.
