Jarvis deposits of $$ \$ 2500 $$ into each of two savings accounts - Account I pays $$ 5 \% $$ simple annuat interest. - Account II pays 98 interest compounded annually, If Jarvis does not make any additionat deposits or withdrawals, what is the sum of the balances in Account and Account II at the end of 9 year?

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UpStudy AI · Accepted Answer

To find the total balance in both accounts after 9 years, we will calculate the balance for each account separately and then sum them up.

### Account I: Simple Interest
The formula for calculating the balance with simple interest is:

$$
A = P(1 + rt)
$$

Where:
- $$ A $$ = the amount of money accumulated after n years, including interest.
- $$ P $$ = principal amount (the initial amount of money).
- $$ r $$ = annual interest rate (decimal).
- $$ t $$ = time the money is invested or borrowed for, in years.

For Account I:
- $$ P = 2500 $$
- $$ r = 0.05 $$ (5% as a decimal)
- $$ t = 9 $$

Now, we can calculate the balance for Account I.

### Account II: Compound Interest
The formula for calculating the balance with compound interest is:

$$
A = P(1 + r)^t
$$

Where:
- $$ A $$ = the amount of money accumulated after n years, including interest.
- $$ P $$ = principal amount (the initial amount of money).
- $$ r $$ = annual interest rate (decimal).
- $$ t $$ = number of years the money is invested or borrowed.

For Account II:
- $$ P = 2500 $$
- $$ r = 0.98 $$ (98% as a decimal)
- $$ t = 9 $$

Now, we can calculate the balance for Account II.

Let's perform the calculations for both accounts.
Calculate the value by following steps:
- step0: Calculate:
  $$2500\left(1+0.05\times 9\right)$$
- step1: Multiply the numbers:
  $$2500\left(1+0.45\right)$$
- step2: Add the numbers:
  $$2500\times 1.45$$
- step3: Multiply the numbers:
  $$3625$$
Calculate or simplify the expression $$ 2500*(1 + 0.98)^9 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2500\left(1+0.98\right)^{9}$$
- step1: Add the numbers:
  $$2500\times 1.98^{9}$$
- step2: Convert the expressions:
  $$2500\left(\frac{99}{50}\right)^{9}$$
- step3: Simplify:
  $$2500\times \frac{99^{9}}{50^{9}}$$
- step4: Rewrite the expression:
  $$50^{2}\times \frac{99^{9}}{50^{9}}$$
- step5: Reduce the numbers:
  $$1\times \frac{99^{9}}{50^{7}}$$
- step6: Multiply:
  $$\frac{99^{9}}{50^{7}}$$
### Calculations

1. **Account I (Simple Interest)**:
   $$
   A = 2500(1 + 0.05 \times 9) = 2500(1 + 0.45) = 2500 \times 1.45 = 3625
   $$
   So, the balance in Account I after 9 years is **\$3625**.

2. **Account II (Compound Interest)**:
   $$
   A = 2500(1 + 0.98)^9 \approx 2500 \times 1169302.076779 \approx 2923255.19
   $$
   So, the balance in Account II after 9 years is approximately **\$1169302.08**.

### Total Balance
Now, we sum the balances from both accounts:
$$
\text{Total Balance} = 3625 + 1169302.08 \approx 1172927.08
$$

Thus, the sum of the balances in Account I and Account II at the end of 9 years is approximately **\$1172927.08**.
The total balance in both accounts after 9 years is approximately \$1,172,927.08.

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