Question

Compute the interest rate at which $500 per month payments should grow to accumulate savings of $100,000 in 7 years. Payments are made at the end of each month. (Note: Round your answer to two decimal places.) RATE DISC NOMINAL EFFECT A B 1 Data Description 2 NPER 7 x 12 = 84 3 PMT 500 4 PV 0 5 FV 100,000 6 [Type] 0 7 Interest Rate =EFFECT(1.87%, B5) 8 = %

Answer 1

Answer:

The interest rate=13.19%

Explanation:

Step 1: Calculate the present value of the investment

Present value=monthly payments×number of months in a year×number of years

where;

monthly payments=$500

number of months in a year=12

number of years=7

replacing;

Present value=(500×12×7)=42,000

Present value=$42,000

Step 2: Get interest rate

Using the formula below;

FV=PV(1+r)^n

where;

FV=future value of the investment=$100,000

PV=present value=$42,000

r=unknown

n=7

replacing;

100,000=42,000{(1+r)^7}

(100,000/42,000)=(1+r)^7

(100/42)^(1/7)=1+r

1.1319=1+r

r=1.1319-1

r=0.1319

The interest rate=0.1319×100=13.19%

The interest rate=13.19%