Respuesta :
Answer:
The value for partners savings bank at the end of 1 year is $12,362.70. The value for Selwyn's at the end of 1 year is $12,334.58. The future value obtained by investing in Partners Saving Bank is more as compared to Selwyn’s Saving Bank. Hence Joseph is recommended to choose Partners Saving Bank.
Step-by-step explanation:
The value of the interest rate and the compounding applied, gives the
value in the account after one year.
- The value of the account with Partner's Bank after one year is approximately $12,362.7, which is higher than the value in the Selwyn's account.
- The value in Selwyn's which after one year is $12,344.58.
- Joseph should choose the Partner's Bank account
Reasons:
The amount Joseph receives as gift, A₀ = $12,000
Amount interest from Partner's Savings Bank, r = 3% compounded semiannually
Interest rate offered by Selwyn's, r = 2.75% compounded continuously
Required:
The value of the two account at the end of one year.
Solution:
[tex]A_t = A_0 \cdot \left(1 + \dfrac{r}{2} \right)^{2 \times t}[/tex]
The amount at the end of one year (t = 1) in Partner's Savings Bank is therefore;
[tex]A_t = 12,000 \times \left(1 + \dfrac{0.03}{2} \right)^{2 \times 1} = 12,362.7[/tex]
- The value in the Partner's Savings Bank after one year, A(t) ≈ $12,362.7
The value of an account at Selwyn's is therefore;
The interest rate compounded continuously is presented as follows;
[tex]A(t) = \mathbf{A_0 \cdot e^{r \cdot t}}[/tex]
A₀ = The original amount invested = $12,000
Which gives;
[tex]A(t) = 12,000 \times e^{0.0275 \times 1} \approx \mathbf{12,334.58}[/tex]
- The value of the account at Selwyn's after one year, A(1) ≈ $12334.58
- Therefore, the account Joseph should choose is the Partner's Savings Bank that gives a higher value in the account after one year.
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