If $15,000 is invested at an interest rate of 10% per year, compounded monthly, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
a. 6 years
b. 12 years
c. 18 years
I saw it would be c 18 years
What are you talking about?
15,000 (1 + 0.10/12)^12n
for 6 years
15,000(1.008333)^72 = 15,000*1.8176
= $ 27,263.91
for 12 years
15,000 (1.008333)^144 = $49,554.73 etc
To find the value of the investment after a given number of years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount P is $15,000, the annual interest rate r is 10% (or 0.10 as a decimal), and the interest is compounded monthly, so n = 12.
a. To find the value after 6 years:
t = 6
A = 15000(1 + 0.10/12)^(12*6)
Calculating the expression inside the parentheses:
(1 + 0.10/12) = 1.00833333333
Calculating (1 + 0.10/12)^(12*6):
(1.00833333333)^(72) = 1.61162224098
Multiplying the principal amount by the calculated value:
A = 15000 * 1.61162224098 = $24,174.33
Therefore, the value of the investment after 6 years is approximately $24,174.33.
b. To find the value after 12 years:
t = 12
A = 15000(1 + 0.10/12)^(12*12)
Calculating the expression inside the parentheses:
(1 + 0.10/12) = 1.00833333333
Calculating (1 + 0.10/12)^(12*12):
(1.00833333333)^(144) = 3.17204699726
Multiplying the principal amount by the calculated value:
A = 15000 * 3.17204699726 = $47,580.70
Therefore, the value of the investment after 12 years is approximately $47,580.70.
c. To find the value after 18 years:
t = 18
A = 15000(1 + 0.10/12)^(12*18)
Calculating the expression inside the parentheses:
(1 + 0.10/12) = 1.00833333333
Calculating (1 + 0.10/12)^(12*18):
(1.00833333333)^(216) = 8.26222165461
Multiplying the principal amount by the calculated value:
A = 15000 * 8.26222165461 = $123,933.25
Therefore, the value of the investment after 18 years is approximately $123,933.25.