Question

Ingrid wants to buy a ​$17000 car in 5 years. How much money must she deposit at the end of each quarter in an account paying ​5.9% compounded quarterly so that she will have enough to pay for her​ car?

Answer 1

The rate of interest is 5.9% compounded quarterly

So The rate of interest per quarter or period (R) = 5.9/4 = 1.475% or 0.01475

The time period is 5 years

The number of quarters per year=4

So the total number of periods (n ) = 5*4 = 20

Here Ingrid wants to accumulate $ 17000 in 5 years

so Future value (FV) =$ 17000

We have to find the annuity payment (PMT) he has to make per quarter

According to the formula,

FV = PMT* [ (1+ R)ⁿ - 1 ] / R

or, $ 17000 = PMT * [(1 + 0.01475)²⁰ -1 ] / 0.01475

or $ 17000 = PMT* [(1.01475)²⁰ - 1 ] / 0.01475

or, $ 17000 =PMT * 23.06683

PMT = $ 17000 / 23.06683 = $ 736.988975

So she must deposit $ 736.988975 or $ 736.989 (rounding to 3 decimals) per quarter (Answer)