Question

Sam is trying to save money to buy a new $8,500 smartphone. Sam has $5,800 that can be invested at either Bank A or Bank B. Bank A pays monthly interest of 0.65 percent, compounded monthly on its account. Bank B pays 8 percent simple interest on its account.

(a)How long does it take for having enough money for buying Sam’s smartphone at Bank A and Bank B respectively?

(b)Based on your answer in part (a), which bank should Sam choose to save money for his purchase of the smartphone? Explain.

(c)A phone sales representative proposes a third option to Sam, in which Sam can immediately enjoy the $8,500 smartphone by signing a 12-month loan installment of $750 occurring one month from now. What is its annual percentage rate (APR)? What is its effective annual rate (EAR)

Answer 1

a]

Bank A

future value = present value * (1 + r)n

where r = periodic rate of interest

n = number of periods

$8,500 = $5,800 * (1 + 0.65%)n

1.0065n = (8,500 / 5,800)

n = log1.0065(8,500 / 5,800)

n = 59

Number of years = 59 / 12 = 4.92 years

It will take 4.92 years to have enough money at Bank A

Bank B

Ending amount = beginning amount * (1 + (interest rate * number of years))

Let us say the number of years is N. Then :

$8,500 =  $5,800 * (1 + (8% * N))

$8,500 =  $5,800 + 464N

N = 5.82

It will take 5.82 years to have enough money at Bank B

b]

Sam should choose Bank A because it takes a shorter time to have enough money to buy the smartphone.

c]

Monthly rate is calculated using RATE function in Excel :

nper = 12 (number of monthly instalments)

pmt = -750 (Monthly instalment. This is entered with a negative sign because it is a payment)

pv = 8500 (cost of smartphone)

RATE is calculated to be 0.89%

This is the monthly rate. APR = monthly rate * 12 = 0.89% * 12 = 10.69%

A1 X fx =RATE(12,-750,8500)*12 B C D A 10.69% 1)

EAR = (1 + (APR/n))n - 1

where n = number of compounding periods per year. This is 12, as the compounding is monthly (since the payments are monthly)

EAR = (1 + (10.69%/12))12 - 1

EAR = 11.23%