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5. In January of 2003. Jaylen deposited $1,450 into an investment account earning 5% interest.

compounded semiannually. If there are no other deposits or withdrawals from the account,
find the total interest earned by the end of December in 2017.

1 Answer

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Answer:

Explanation:

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According to The Calculator Site, the formula for compound interest is:

A = P (1 + r/n)^nt

where

A = future value of the investment

P = principal amount

r = annual interest rate (decimal)

n = number of times interest is compounded per year

t = time in years

To find the total interest earned, we need to subtract the principal amount from the future value. The formula for total interest is:

I = A - P

where

I = total interest

Now, we can plug in the given values into the formulas. We have:

P = $1,450

r = 0.05

n = 2 (semiannually means twice a year)

t = 15 (from January 2003 to December 2017)

First, we calculate the future value using the compound interest formula:

A = P (1 + r/n)^nt

A = 1450 (1 + 0.05/2)^(2 x 15)

A = 1450 (1.025)^30

A = 1450 x 2.098

A = $3042.10

Then, we calculate the total interest by subtracting the principal amount from the future value:

I = A - P

I = 3042.10 - 1450

I = $1592.10

Therefore, the total interest earned by the end of December in 2017 is $1592.10.

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