Question

In: Finance

You expect that you will need to replace your furnace in 4 years at a cost...

You expect that you will need to replace your furnace in 4 years at a cost of $15,682. How

much must you save today in an account that pays 3.58% APR (compounded monthly) to exactly pay the $15,682 in 4 years?

Solutions

Expert Solution

Solution:

Compound Interest or Interest on Interest is the amount of interest on deposit or loan calculated based on both the initial principal amount and accumulated interest thereon from previous periods.

Formula for calculation of future value of saving to be made today  : FV = PV × (1+r)n

Where:                FV      = Future Value

                        PV   = Present Value

                        r        = Annual Interest Rate

                        n         = Number of periods

Given: FV. =  $15,682

PV       = ?

                        r          = 3.58% p.a.

                        n         = 4 Years

If compound interest is calculated on monthly basis then the formulas turns to

FV = PV × (1+r/12)12*n

By substituting values in formula, we get

$15,682 = PV x (1+ .0358/12)12*4  

PV =  $15,682 / (1.002983)48  

PV. = $13,592.78

Therefore you must save today an amount of $13,592.78 in an account that pays 3.58% APR (compounded monthly) to exactly pay the $15,682 in 4 years to replace the furnace.

jeff jeffy answered 1 year ago
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