Question

Zhan has a credit card charge of $250 on a card that charges 19% annual interest compounded daily. If he makes no other charges or payments on the account, what would be the balance of his account in 1 year? Round to the nearest whole dollar.

Explain your answer please :)

Answer 1

`\$302`

Explanation:

we know that

The compound interest formula is equal to

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

where

A is the Final balance in the account

P is the credit card charge

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=1\ years\\ P=\$250\\ r=19\%=19\100=0.19\\n=365`

substitute in the formula above

`A=250(1+(0.19)/(365))^(365*1)`

`A=250((365.19)/(365))^(365)`

`A=\$302.30`

Round to the nearest whole dollar.

`A=\$302`

Answer 2

The balance of Zhan's account in 1 year would be $ 302

Explanation:

1. Let's review the information given to us to answer the question correctly:

Credit charge = $ 250

Interest rate = 19% compounded daily = 0.19/365 = 0.000520548

2. If Zhan makes no other charges or payments on the account, what would be the balance of his account in 1 year? Round to the nearest whole dollar.

Let's use the compound interest formula this way:

A = P * (1 + r/n) ⁿˣ, where:

A = final balance of the credit card

P = initial charge ($ 250)

r = interest rate (0.19)

n = number of times interest applied per time period (365 days)

x = number of time periods elapsed (1 year)

Replacing with the values we know we have:

A = 250 * (1 + 0.19/365)³⁶⁵

A = 250 * (1.000520548)³⁶⁵

A = 250 * 1.20918982

A = 302.297455

A = 302 (rounding to the nearest whole dollar)