Problem PageQuestionAn amount of US$19.000 is borrowed for 8 years at 5,25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back

To solve this problem, we need to use the formula for compound interest. The formula is:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

where:

• $A$ is the amount of money accumulated after n years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

Given:

• $P = 19,000$ USD
• $r = 5.25\% = 0.0525$
• $n = 1$ (since the interest is compounded annually)
• $t = 8$ years

Now, plug these values into the formula:

$A = 19,000 \left(1 + \frac{0.0525}{1}\right)^{1 \times 8}$

Simplify inside the parentheses:

$A = 19,000 \left(1 + 0.0525\right)^{8}$

$A = 19,000 \left(1.0525\right)^{8}$

Calculate $(1.0525)^{8}$:

$(1.0525)^{8} \approx 1.48024$

Now multiply by the principal amount:

$A = 19,000 \times 1.48024$

$A \approx 28,124.56$

Therefore, the amount that must be paid back at the end of the 8-year period is approximately US$28,124.56.