$10,000 was deposited into an investment account earning interest at a nominal rate of 9% compounded monthly for eight years.How much interest was earned in the fifth year?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for calculating compound interest:

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

where:
A = the total amount (known as the future value) 
P = the principal amount (the initial deposit) 
r = the nominal interest rate (as a decimal) 
n = the number of times the interest is compounded per year 
t = the number of years

We know that P = $10,000, r = 0.09, and n = 12 (because the interest is compounded monthly). We want to find out the interest earned in the fifth year, which means we need to calculate the future value of the initial deposit after 5 years and then subtract the principal amount from it.

To find the future value after 5 years, we set t = 5 in the formula:

A = 10,000(1 + 0.09/12)^(12*5) 
A = 10,000(1.0075)^60 
A = $16,208.98 (rounded to the nearest cent)

Now we can subtract the principal amount from the future value to find the interest earned:

interest = $16,208.98 - $10,000 
interest = $6,208.98

Since we're asked to find the interest earned in the fifth year only, we need to subtract the interest earned in the fourth year (which we can calculate using the same method) from the total interest earned over 5 years:

interest earned in fifth year = total interest earned over 5 years - interest earned in fourth year

Using the same formula as before with t = 4, we find that the future value after 4 years is:

A = 10,000(1 + 0.09/12)^(12*4) 
A = 10,000(1.0075)^48 
A = $13,966.22 (rounded to the nearest cent)

So the interest earned in the fourth year is:

interest earned in fourth year = $13,966.22 - $10,000 
interest earned in fourth year = $3,966.22

Therefore, the interest earned in the fifth year is:

interest earned in fifth year = $6,208.98 - $3,966.22 
interest earned in fifth year = $2,242.76

The answer is closest to B) $1342.76.

$10,000 Was Deposited into an Investment Account Earning Interest at a Nominal