Answer:
FV = 2762.07
Step-by-step explanation:
Use the equation for amount after compound interest
"A" is the amount, same as future value, like the <u>total</u>
"P" is the principal, the <u>starting amount</u> or initial investment or loan
"i" is the <u>interest rate</u> earned each compounding period, in decimal form
"n" is the <u>number of compounding periods</u>
A = ?
P = 2500
The interest rate is calculated by dividing the annual interest rate in decimal form by the compounding frequency (how many times interest is calculated each year)
i = r/c
Find "r". The annual interest rate is 2,5%. To convert it to decimal form, divide it by 100.
r = 2,5% = 0.025
"c" is the compounding frequency. The problem states "compounded quarterly", meaning 4 times a year.
c = 4
Substitute r and c into the formula
i = r/c
i = 0.025/4
i = 0.00625
The number of compounding periods is calculated by multiplying the time in years by the compounding frequency (how many times interest is calculated each year)
n = tc
The problem states it was compounded for "4 years".
t = 4
It was compounded quarterly.
c = 4
Substitute c and t into the formula
n = tc
n = (4)(4)
n = 16
Now that we know all of the variables' values except for one, we can solve for the missing variable, "A", future value.
Substitute P, i, and n into the formula:
A = P(1+i)ⁿ
A = 2500(1+0.00625)¹⁶ Solve inside the brackets
A = 2500(1.00625)¹⁶ Enter into calculator. Do the exponent first, then multiply by 2500.
A = 2762.07 Answer, rounded off to two decimal places
Since A = FV, the future value is ₴2762.07.