Question

Grabiel deposits 2500 into each of two saving accouts accout i earns 4percent annual simple interst accout ll earns 4 percent compounded annually Gabrel does not make any other deposists or withdraws what is the sum balance in accout i and account ll at the end of 3 yearsf 5600.00g5612.16h5624.32j5200.00

Answer 1

Gabriel deposits 2500 into two accounts i and ii, for 3 years. Account i has a 4% simple interest rate and account ii has a 4% compound interest (annually)

To determine the sum of both accounts' balances after a 3-year time period, the first step is to calculate how much will the Accrued amount be for both accounts.

Account i:

To determine the accrued amount for an account with the simple interest you have to use the following formula:

`A=P(1+rt)`

Where

A is the accrued amount after t time intervals

P is the principal amount

r is the interest rate (expressed as a decimal value)

t is the time interval (measured in years)

The principal amount is P=2500

The interest rate expressed as a decimal value:

`r=(4)/(100)=0.04`

The time period is t=3 years.

Replace the information on the formula to calculate the accrued amount for account i:

`\begin{gathered} A_i=2500(1+0.04\cdot3) \\ A_i=2500(1+0.12) \\ A_i=2500\cdot1.12 \\ A_i=2800 \end{gathered}`

After 3 years the balance for account i will be Ai=$2800

Account ii

To calculate the accrued amount for an account that compounds annually you have to use the following formula:

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

Where

A is the accrued amount

P is the principal amount

r is the interest rate expressed as a percentage

n is the number of compound periods per unit of time

t is the time periods measured in years

For this account:

P=2500

r=4/100=0.04

n=1 → the account compounds annually, which means that there is one compound period per year

t=3 years

`\begin{gathered} A_(ii)=2500(1+(0.04)/(1))^(1\cdot3) \\ A_(ii)=2500(1+0.04)^3 \\ A_(ii)=2500(1.04)^3 \\ A_(ii)=2500\cdot1.12 \\ A_(ii)=2812.16 \end{gathered}`

After 3 years the balance for account ii will be Aii=$2812.16

Now what's left is to add both amounts to determine the final balance between both accounts:

`A_i+A_(ii)=2800+2812.16=5612.16`

The final balance will be $5612.16