You deposit $45,000 into a savings account that pays 2.5% annual interest. Find the balance after 20 years if the interest rate is compounded monthly. Round your answer to the nearest hundredth.

Answer 1

A = amount in t years

P = principal (starting value)

r = annual interest rate (in decimal form)

n = number of compounding per year

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

So. amount in 20 years = 45000(1 + 0.025/12)^(12)(20)

= 45000(1.00208333)²⁴⁰

Evaluate on your calculator.

Answer 2

Please see below for a code-formatted answer:

You need to use the formula for compound interest:

/* Compound Interest Formula */

A = P * (1 + r / n) ^ (n * t)

/* Given values */

P = 45000; /* Principal amount (deposited amount from the word problem)*/

r = 0.025; /* Annual interest rate in decimal form (2.5% percent in the word problem) */

n = 12; /* Number of times interest is compounded per year (compounded monthly in the word problem) */

t = 20; /* Time in years */

We are trying to solve for A.

/* Step 1: Compute the monthly interest rate */

monthly_rate = r / n; /* 0.025 / 12 */

/* Step 2: Add 1 to the monthly interest rate */

rate_plus_one = 1 + monthly_rate; /* 1 + (0.025 / 12) */

/* Step 3: Calculate the total number of compounding periods */

power = n * t; /* 12 * 20 */

/* Step 4: Raise the rate_plus_one to the power of the total periods */

growth_factor = rate_plus_one ** power;

/* Step 5: Multiply the principal by the growth factor */

A = P * growth_factor;

/* Step 6: Round to the nearest hundredth */

A_rounded = round(A, 2); /* Final Balance */

I hope this helps!