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Gabriel deposits $2,500 into each two savings accounts, account 1 earns 4% simple interest, account 2 earns 4% compound interest annually . Gabriel does not make any additional deposits or withdrawals. What is the sum of the balances of account 1 and account 2 at the end of 3 years?

Sagot :

samuelonum1

Answer:

See the answers below

Step-by-step explanation:

Given data

Account 1 SImple interest

P= $2500

R=4%

T= 3 years

A=P(1+rt)

A=2500(1+0.04*3)

A=2500(1+0.12)

A=2500*1.12

A= $2800

Account 2 compound interest

P= $2500

R=4%

T= 3 years

A= P(1+r)^t

A=2500(1+0.04)^3

A=2500(1.04)^3

A=2500*1.124864

A= $2812.16

Answer: the answer is $5.612.16

Step-by-step explanation: Part 1) Account I earns 4% annual simple interest.

we know that

The simple interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

substitute in the formula above

Part 2) Account II earns 4% interest compounded annually.

we know that    

The compound interest formula is equal to  

A=P(1+rt)

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

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=3 years

p=$2,500

r=4%=4/100=0.04

substitute in the formula above  

A=2,500(1+0.04 * 3)

A=2,500 (1.12)

A=$2,800

Part 3) What is the sum of the balances of Account I and Account II at the end of 3 years?

Sum the two final investment

$2,800 + $2,812.16 = $5.612.16

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