1. What lump sum was deposited first in a bank that offers a 5% interest compounded monthly to be able to withdraw 4605 birr per month at the end of each month for 13 years?
monthly rate = .05/12 = .0041666...
n = 12*13 = 156
withdrawal = 4605
Present value = 4605( 1 - 1.0041666..^-156)/.0041666...
= 527455.34
To calculate the initial lump sum that needs to be deposited in a bank, we can use the formula for the future value of an annuity.
The future value of an annuity formula is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value of the annuity
P = Payment per period
r = Interest rate per period
n = Number of periods
In this case, we know that the payment per period is 4605 birr, the interest rate per period is 5%/12 (since it is compounded monthly), and the number of periods is 13 years * 12 months/year = 156 months.
Substituting the values into the formula:
FV = 4605 * ((1 + 0.05/12)^156 - 1) / (0.05/12)
Using a calculator, the future value of the annuity (FV) is approximately 1,260,773 birr.
So, the initial lump sum that needs to be deposited in the bank is 1,260,773 birr.