Question

A bank offers two types of investment to its savers. The first type of investment pays 5% interest compounded quarterly; while in the second type of investment, pay 3% compound interest with continuous capitalization. Considering the term of 1 year, which of the 2 types of investment generates the highest final amount, and consequently yield? A)capitalization yields 3%

b) capitalization yields 5%

Answer 1

FV = PV (1+r)^n

Particulars	Amount
Cash Flow	1000.00
Int Rate	1.250%
Periods	4
Future Value = Cash Flow * ( 1 + r )^n
= $ 1000 ( 1 + 0.0125) ^ 4
= $ 1000 ( 1.0125 ^ 4)
= $ 1000 * 1.0509
= $ 1050.95

Continious Capializaion

FV = PV * e^rt

= 1000 * e^0.03 * 1

= 1000 * e^0.03

= 1000 * 1.0305

= $ 1030.5

Yeild in First Case

= (1+r)^n-1

= (1+0.0125)^4 -1

= (1.0125)^4 -1

= 1.0509-1

= 5.09%

Yeild in Second Case

e^rt -1

e^0.03 *1 -1

e^0.03 -1

1.0305 -1

= 3.05%

Pls do rate, if the answer is correct and comment, if any further assistance is required.