## The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. A. Find how

Question

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate.
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
Principal= \$7000
Rate= 4%
Compounded= Semiannually
Time= 3 years

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3 weeks 2021-10-04T10:46:46+00:00 1 Answer 0

A) Amount in the account after 3 years = \$ 7, 883.14

B)  Interest earned = \$ 883.14

Step-by-step explanation:

The formula to be used is given as

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

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

In the question we are given the following values :

A = final amount = Unknown

P = initial principal balance = \$7,000

r = interest rate = 4% = 0.04

n = number of times interest applied per time period = semi annually , n= 2

t = number of time periods elapsed = 3 years

A) Find how much money there will be in the account after the given number of years.

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

A = \$7,000 (1 + 0.04/2)²×³

A = \$7,000( 1+ 0.04/2)⁶

A = \$7,000( 1.02)⁶

A = \$ 7,883.14

The amount in the account after 3 years = \$ 7,883.14

B. Find the interest earned.

To find the interest earned, we use the formula

A = P + I where

P (principal) = \$ 7,000.00

A (Amount after 3 years) = \$ 7,883.14

I = A – P

I = \$ 7,883.14 – \$ 7,000.00

I =\$ 883.14

The interest earned = \$ 883.14