Question

1. a) Suppose on January 1 you deposit $2,750 in an account that pays a quoted interest rate of 2.35% (APR), with interest added (compounded) daily. How much will you have in your account on October 1, or after 9 months? (assume N = 273 days) Recall that the interest rate (I/Y) represents the periodic rate based on how many times per YEAR the interest is compounded. Hint, this is 365 times per year. As above, and all TVM type problems, there should be no interim rounding of the interest rates.

b) Now suppose you leave your money in the bank for 21 months. Thus, on January 1 you deposit $2,750 in an account that pays an APR of 2.35% compounded daily. How much will be in your account on October 1 of the following year? (assume N = 638 days)

Answer 1

The compound interest formula is: A = P (1 + r/n)^nt

Where, A = Future value of investment

              P = Principal Amount depositing at the beginning

              r = Annual interest rate

              n = no of compounding periods in an year

t = no. of years compounding

a) Amount deposited in January 1st (P) = $ 2,750

Annual interest rate (r) = 2.35%

no of compounding periods in an year (n)= 365

  Future value of investment (A) = P (1 + r/n)^nt

⁼ $ 2,750 (1+0.0235/365)²⁷³

⁼ $2,750 x 1.0177

= $ 2798.76

b) Now suppose you leave your money in the bank for 21 months. Thus, on January 1 you deposit $2,750 in an account that pays an APR of 2.35% compounded daily. How much will be in your account on October 1 of the following year? (assume N = 638 days)

Future value of investment (A) = P (1 + r/n)^nt

⁼ $ 2,750 (1+0.0235/365)⁶³⁸

= $ 2750 x 1.0419

= $23865.31