Mary sought for advice from a friend, a manager of first bank who advi...
Computation of Annual Savings, Duration of Savings, and Interest Rate
Annual Savings
To compute the annual savings, we need to use the present value formula. We know that the present value of Mary's savings in First Bank is 44,914.30 and she saves 12,000 annually. Therefore, the annual savings can be computed as follows:
PV = (PMT / r) x (1 - (1 + r)^-n)
where PV is the present value, PMT is the annual savings, r is the interest rate, and n is the number of years.
Substituting the values we know, we get:
44,914.30 = (12,000 / r) x (1 - (1 + r)^-n)
Using trial and error or a financial calculator, we can solve for r to get the annual interest rate.
Duration of Savings
Since Mary is saving the same amount with the same interest rate in both First Bank and Union Bank, we can assume that the duration of her savings in Union Bank is also 6 years. Therefore, the duration of savings in Union Bank is 6 years.
Annual Interest Rate
Using the present value formula and the given present value of Mary's savings in First Bank, we can solve for the annual interest rate. Once we know the interest rate, we can use it to compute the annual savings in Union Bank.
Therefore, the annual interest rate can be computed as follows:
PV = (PMT / r) x (1 - (1 + r)^-n)
44,914.30 = (12,000 / r) x (1 - (1 + r)^-6)
Using trial and error or a financial calculator, we can solve for r to get the annual interest rate. Once we know the interest rate, we can use it to compute the annual savings in Union Bank.