A firm will need 300,000 at the end of 3 years to repay a loan. The firm decides to deposit 20,000 each quarter during these 3 years into an account which yields 16% per annum compounded quarterly. Will the firm accumulate enough amount in this account to pay the loan of the end of 3 years?
To determine whether the firm will accumulate enough amount in the account to pay the loan at the end of 3 years, we need to calculate the future value of the deposits made every quarter.
The interest rate per quarter is 16% divided by 4, which is 4%.
The number of quarters in 3 years is 3 years multiplied by 4 quarters, which is 12 quarters.
Using the future value of annuity formula, which is:
FV = P * ((1 + r)^n - 1) / r
FV: Future Value
P: Quarterly deposit
r: Interest rate per quarter
n: Number of quarters
We can calculate the future value of the deposits as follows:
FV = 20,000 * ((1 + 0.04)^12 - 1) / 0.04
= 20,000 * (1.04^12 - 1) / 0.04
≈ 20,000 * (1.601031 - 1) / 0.04
≈ 20,000 * (0.601031) / 0.04
≈ 300,515.75
The future value of the deposits after 3 years is approximately 300,516.
Since this amount is greater than the loan amount of 300,000, the firm will accumulate enough in this account to pay off the loan at the end of 3 years.