Question

Assume you are planning to open a saving account to earn interest. Both local banks have
an annual interest rate of 4%. But Bank A’s interest compounds monthly and Bank B’s
interest compounds quarterly.
a. Which bank would you prefer based on their annual effective interest rate?

b. if you need $26,000 as a down payment for a house 4 years later from now. You can
either deposit one lump sum today for this purpose or you can wait for a year and deposit
a lump sum. How much additional money must you deposit if you wait for one year
rather than making the deposit today?

Answer 1

Ans:- (a) EAR annual Interest rate is given by ( 1 + r/n )^n - 1, where r is the annual rate and n is the number of times compounding in a year.

The EAR for Bank A will be ( 1 + 0.04 / 12 ) ^12 - 1 = 0.04074 * 100 = 4.074%

The EAR for Bank B will be ( 1 + 0.04 / 4 )^4 - 1 = 0.04060 = 4.060%.

From the above analysis Bank A should be preferred because its EAR is higher than Bank B.

(b) we need to find how much additional money needs to be deposit if we wait for one year later from now. we will find the PV of down payment today and 1 year later considering $26,000 as future value. The rate is given 4%.

FV = $26,000, Rate = 4%, nper will be 4 for today and 3 for 1 year after.

Therefore the additional amount will be $889.0

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