Question

In: Economics

Someone deposits $200 every 6 months into an account that pays interest at 4% per year...

Someone deposits $200 every 6 months into an account that pays interest at 4% per year compounded quarterly. How much does this person have after 10 years?

Solutions

Expert Solution

Explanation : To find the future value we use following formula


Where,
FV = Future Value

A = Regular Withdrawal Amount OR Regular Interest OR Regular Dividend OR Installment Amount

n = Number of Years/Period

r = Compound Interest Rate

r(p)=Annual Nominal Rate of Interest

Given :
Number of Periods/Years (n) = 10

Nominal Rate Of Interest (r(4)) = 4%

Regular Withdrawal (A) = $ 400

Benefit paid annually

A=200∗2=400


Calculating Effective Interest Rate
Effective Interest can be calculated by following formula,


where
r=Effective Rate of Interest

r(p)=Nominal rate of interest compounded p- times a year

Therefore,

Calculating Nominal Interest Rate
Nominal Interest can be calculated by following formula,


where
r=Effective Rate of Interest

r(p)=Nominal rate of interest compounded p- times a year

Therefore,

After substituting the values into the formula we have,

The future value is $4864.

Rahul Sunny answered 2 years ago
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